Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
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    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 43)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 16)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 20)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 21)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 9)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 6)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 15)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
British Journal of Mathematics & Computer Science     Full-text available via subscription   (Followers: 1)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 2)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 1)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 20)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 3)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 10)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Doklady Akademii Nauk     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Algebra Universalis
Journal Prestige (SJR): 0.583
Citation Impact (citeScore): 1
Number of Followers: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1420-8911 - ISSN (Online) 0002-5240
Published by Springer-Verlag Homepage  [2467 journals]
  • Another look on tense and related operators

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      Abstract: Abstract Motivated by the classical work of Halmos on functional monadic Boolean algebras, we derive three basic sup-semilattice constructions, among other things, the so-called powersets and powerset operators. Such constructions are extremely useful and can be found in almost all branches of modern mathematics, including algebra, logic, and topology. Our three constructions give rise to four covariant and two contravariant functors and constitute three adjoint situations we illustrate in simple examples.
      PubDate: 2022-11-01
       
  • The assembly of a pointfree bispace and its two variations

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      Abstract: Abstract We explore a pointfree theory of bitopological spaces (that is, sets equipped with two topologies). In particular, here we regard finitary biframes as duals of bitopological spaces. In particular for a finitary biframe \(\mathcal {L}\) the ordered collection of all its pointfree bisubspaces (i.e. its biquotients) is studied. It is shown that this collection is bitopological in three meaningful ways. In particular it is shown that, apart from the assembly of a finitary biframe \(\mathcal {L}\) , there are two other structures \(\mathsf {A}_{cf}(\mathcal {L})\) and \(\mathsf {A}_{\pm }(\mathcal {L})\) , which both have the same main component as \(\mathsf {A}(\mathcal {L})\) . The main component of both \(\mathsf {A}_{cf}(\mathcal {L})\) and \(\mathsf {A}_{\pm }(\mathcal {L})\) is the ordered collection of all biquotients of \(\mathcal {L}\) . The structure \(\mathsf {A}_{cf}(\mathcal {L})\) being a biframe shows that the collection of all biquotients is generated by the frame of the patch-closed biquotients together with that of the patch-fitted ones. The structure \(\mathsf {A}_{\pm }(\mathcal {L})\) being a biframe shows the collection of all biquotients is generated by the frame of the positive biquotients together with that of the negative ones. Notions of fitness and subfitness for finitary biframes are introduced, and it is shown that the analogues of two characterization theorems for these axioms hold. A spatial, bitopological version of these theorems is proven, in which finitary biframes whose spectrum is pairwise \(T_1\) are characterized, among other things in terms of the spectrum \(\mathsf {bpt}(\mathsf {A}_{cf}(\mathcal {L}))\) .
      PubDate: 2022-10-08
       
  • Uniform continuity of pointfree real functions via farness and related
           Galois connections

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      Abstract: Abstract This paper concerns uniform continuity of real-valued functions on a (pre-)uniform frame. The aim of the paper is to characterize uniform continuity of such frame homomorphisms in terms of a farness relation between elements in the frame, and then to derive from it a separation and an extension theorem for real-valued uniform maps on uniform frames. The approach, purely order-theoretic, uses properties of the Galois maps associated with the farness relation. As a byproduct, we identify sufficient conditions under which a (continuous) scale in a frame with a preuniformity generates a real-valued uniform map.
      PubDate: 2022-10-03
       
  • Choice-free duality for orthocomplemented lattices by means of spectral
           spaces

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      Abstract: Abstract The existing topological representation of an orthocomplemented lattice via the clopen orthoregular subsets of a Stone space depends upon Alexander’s Subbase Theorem, which asserts that a topological space X is compact if every subbasic open cover of X admits of a finite subcover. This is an easy consequence of the Ultrafilter Theorem—whose proof depends upon Zorn’s Lemma, which is well known to be equivalent to the Axiom of Choice. Within this work, we give a choice-free topological representation of orthocomplemented lattices by means of a special subclass of spectral spaces; choice-free in the sense that our representation avoids use of Alexander’s Subbase Theorem, along with its associated nonconstructive choice principles. We then introduce a new subclass of spectral spaces which we call upper Vietoris orthospaces in order to characterize up to homeomorphism (and isomorphism with respect to their orthospace reducts) the spectral spaces of proper lattice filters used in our representation. It is then shown how our constructions give rise to a choice-free dual equivalence of categories between the category of orthocomplemented lattices and the dual category of upper Vietoris orthospaces. Our duality combines Bezhanishvili and Holliday’s choice-free spectral space approach to Stone duality for Boolean algebras with Goldblatt and Bimbó’s choice-dependent orthospace approach to Stone duality for orthocomplemented lattices.
      PubDate: 2022-08-07
      DOI: 10.1007/s00012-022-00789-y
       
  • A theorem of Mumford and Ramanujam for universal algebras

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      Abstract: Abstract A well-known result in quasigroup theory says that an associative quasigroup is a group, i.e. in quasigroups, associativity forces the existence of an identity element. The converse is, of course, far from true, as there are many, many non-associative loops. However, a remarkable theorem due to David Mumford and C.P. Ramanujam says that any projective variety having a binary morphism admitting a two-sided identity must be a group. Motivated by this result, we define a universal algebra (A; F) to be an MR-algebra if whenever a binary term function m(x, y) in the algebra admits a two-sided identity, then the reduct (A; m(x, y)) must be associative. Here we give some non-trivial varieties of quasigroups, groups, rings, fields and lattices which are MR-algebras. For example, every MR-quasigroup must be isotopic to a group, MR-groups are exactly the nilpotent groups of class 2, while commutative rings and complemented lattices are MR-algebras if and only if they are Boolean.
      PubDate: 2022-08-07
      DOI: 10.1007/s00012-022-00790-5
       
  • Idempotent identities in f-rings

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      Abstract: Abstract Let A be an Archimedean f-ring with identity and assume that A is equipped with another multiplication \(*\) so that A is an f-ring with identity u. Obviously, if \(*\) coincides with the original multiplication of A then u is idempotent in A (i.e., \(u^{2}=u\) ). Conrad proved that the converse also holds, meaning that, it suffices to have \(u^{2}=u\) to conclude that \(*\) equals the original multiplication on A. The main purpose of this paper is to extend this result as follows. Let A be a (not necessary unital) Archimedean f-ring and B be an \(\ell \) -subgroup of the underlaying \(\ell \) -group of A. We will prove that if B is an f-ring with identity u, then the equality \(u^{2}=u\) is a necessary and sufficient condition for B to be an f-subring of A. As a key step in the proof of this generalization, we will show that the set of all f-subrings of A with the same identity has a smallest element and a greatest element with respect to the inclusion ordering. Also, we shall apply our main result to obtain a well known characterization of f-ring homomorphisms in terms of idempotent elements.
      PubDate: 2022-08-05
      DOI: 10.1007/s00012-022-00792-3
       
  • Monounary algebras containing subalgebras with meet-irreducible congruence
           lattice

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      Abstract: Abstract The system of all congruence lattices of all algebras with fixed base set A forms a lattice with respect to inclusion, denoted by \(\mathcal {E}_A\) . Let A be finite. The meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. We assume that (A, f) has a connected subalgebra B such that B contains at least 3 cyclic elements and is meet-irreducible in \({\mathcal {E}}_B\) and we prove several sufficient conditions under which \({{\,\mathrm{Con}\,}}(A, f)\) is meet-irreducible in \({\mathcal {E}}_A\) .
      PubDate: 2022-08-05
      DOI: 10.1007/s00012-022-00786-1
       
  • Lattices of retracts of direct products of two finite chains and notes on
           retracts of lattices

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      Abstract: Abstract Ordered by set inclusion, the retracts of a lattice L together with the empty set form a bounded poset \(Ret (L)\) . By a grid we mean the direct product of two non-singleton finite chains. We prove that if G is a grid, then \(Ret (G)\) is a lattice. We determine the number of elements of \(Ret (G)\) . Some easy properties of retracts, retractions, and their kernels called retraction congruences of (mainly distributive) lattices are found. Also, we present several examples, including a 12-element modular lattice M such that \(Ret (M)\) is not a lattice.
      PubDate: 2022-08-02
      DOI: 10.1007/s00012-022-00788-z
       
  • Improved bounds on the size of the smallest representation of relation
           algebra $$32_{65}$$ 32 65

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      Abstract: Abstract In this paper, we shed new light on the spectrum of the relation algebra we call \(A_{n}\) , which is obtained by splitting the non-flexible diversity atom of \(6_{7}\) into n symmetric atoms. Precisely, show that the minimum value in \(\text {Spec}(A_{n})\) is at most \(2n^{6 + o(1)}\) , which is the first polynomial bound and improves upon the previous bound due to Dodd and Hirsch (J Relat Methods Comput Sci 2:18–26, 2013). We also improve the lower bound to \(2n^{2} + 4n + 1\) , which is roughly double the trivial bound of \(n^{2} + 2n + 3\) . In the process, we obtain stronger results regarding \(\text {Spec}(A_{2}) =\text {Spec}(32_{65})\) . Namely, we show that 1024 is in the spectrum, and no number smaller than 26 is in the spectrum. Our improved lower bounds were obtained by employing a SAT solver, which suggests that such tools may be more generally useful in obtaining representation results.
      PubDate: 2022-07-30
      DOI: 10.1007/s00012-022-00791-4
       
  • The number of languages with maximum state complexity

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      Abstract: Abstract Câmpeanu and Ho (2004) determined the maximum finite state complexity of finite languages, building on work of Champarnaud and Pin (1989). They stated that it is very difficult to determine the number of maximum-complexity languages. Here we give a formula for this number. We also generalize their work from languages to functions on finite sets.
      PubDate: 2022-07-30
      DOI: 10.1007/s00012-022-00785-2
       
  • The structure of completely meet irreducible congruences in strongly
           Fregean algebras

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      Abstract: Abstract A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals projectivity relation in the posets of their completely meet irreducible congruences and show that its cosets have the natural structure of a Boolean group. In particular, this approach allows us to represent congruences and elements of such algebras as the subsets of upward closed subsets of these posets with some special properties.
      PubDate: 2022-07-13
      DOI: 10.1007/s00012-022-00787-0
       
  • Minimum proper extensions in some lattices of subalgebras

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      Abstract: Abstract Let \({\mathcal {A}}\) be a class of algebras with \(I, A \in {\mathcal {A}}\) . We interpret the lattice-theoretic “strictly meet irreducible/cover” situation \(B < C\) in lattices of the form \(S_{{\mathcal {A}}}(I,A)\) of all subalgebras of A containing I, where we call such \(B < C\) a minimum proper extension (mpe), and show that this means B is maximal in \(S_{{\mathcal {A}}}(I,A)\) for not containing some \(r \in A\) and C is generated by B and r. For the class \({\mathcal {G}}\) of groups, we determine the mpe’s in \(S_{{\mathcal {G}}}(\{0\},{\mathbb {Q}})\) using invariants of Beaumont and Zuckerman and show that these (plus utilization of a Hamel basis) determine the mpe’s in \(S_{{\mathcal {G}}}(\{0\},{\mathbb {R}})\) . Finally, we show that the latter yield some (not all) of the minimum proper essential extensions in \(\mathbf {W}^{*}\) , the category of Archimedean \(\ell \) -groups with strong order unit and unit-preserving \(\ell \) -group homomorphisms.
      PubDate: 2022-07-07
      DOI: 10.1007/s00012-022-00784-3
       
  • A finite axiomatization of positive MV-algebras

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      Abstract: Abstract Positive MV-algebras are the subreducts of MV-algebras with respect to the signature \(\{\oplus , \odot , \vee , \wedge , 0, 1\}\) . We provide a finite quasi-equational axiomatization for the class of such algebras.
      PubDate: 2022-06-28
      DOI: 10.1007/s00012-022-00776-3
       
  • Localic transitivity

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      Abstract: Abstract For a dynamical system (X, f), the notion of topological transitivity has been studied by some researchers. There are several definitions of this property, and it is part of the folklore of dynamical systems that under some hypotheses, they are equivalent. In this paper, our aim is to introduce and study some properties of topological transitivity in pointfree topology, for which we first need to define in a way what makes them conservative extensions of topological transitivity defined by G.D. Birkhoff. We describe the way the different properties are related to each other in pointfree topology.
      PubDate: 2022-06-28
      DOI: 10.1007/s00012-022-00783-4
       
  • Difference–restriction algebras of partial functions:
           axiomatisations and representations

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      Abstract: Abstract We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational axiomatisation for the class of algebras representable by partial functions. As a corollary, the same equations axiomatise the algebras representable by injective partial functions. For complete representations, we show that a representation is meet complete if and only if it is join complete. Then we show that the class of completely representable algebras is precisely the class of atomic and representable algebras. As a corollary, the same properties axiomatise the class of algebras completely representable by injective partial functions. The universal-existential-universal axiomatisation this yields for these complete representation classes is the simplest possible, in the sense that no existential-universal-existential axiomatisation exists.
      PubDate: 2022-06-27
      DOI: 10.1007/s00012-022-00775-4
       
  • A relatively finite-to-finite universal but not Q-universal quasivariety

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      Abstract: Abstract It was proved by the authors that the quasivariety of quasi-Stone algebras \(\mathbf {Q}_{\mathbf {1,2}}\) is finite-to-finite universal relative to the quasivariety \(\mathbf {Q}_{\mathbf {2,1}}\) contained in \(\mathbf {Q}_{\mathbf {1,2}}\) . In this paper, we prove that \(\mathbf {Q}_{\mathbf {1,2}}\) is not Q-universal. This provides a positive answer to the following long standing open question: Is there a quasivariety that is relatively finite-to-finite universal but is not Q-universal'
      PubDate: 2022-06-27
      DOI: 10.1007/s00012-022-00782-5
       
  • On relatively elementary definability of graph classes in the class of
           semigroups

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      Abstract: Based on the previously obtained concrete characterization of the endomorphism semigroups of quasi-acyclic reflexive graphs we prove the relatively elementary definability of the class of such graphs in the class of all semigroups. It will permit us to investigate for such graphs the abstract representation problem for the endomorphism semigroups of graphs and the problem of elementary definability of graphs by their endomorphism semigroups.
      PubDate: 2022-06-27
      DOI: 10.1007/s00012-022-00780-7
       
  • Spectral properties of cBCK-algebras

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      Abstract: Abstract In this paper we study prime spectra of commutative BCK-algebras. We give a new construction for commutative BCK-algebras using rooted trees, and determine both the ideal lattice and prime ideal lattice of such algebras. We prove that the spectrum of any commutative BCK-algebra is a locally compact generalized spectral space which is compact if and only if the algebra is finitely generated as an ideal. Further, we show that if a commutative BCK-algebra is involutory, then its spectrum is a Priestley space. Finally, we consider the functorial properties of the spectrum and define a functor from the category of commutative BCK-algebras to the category of distributive lattices with zero. We give a partial answer to the question: what distributive lattices lie in the image of this functor'
      PubDate: 2022-06-27
      DOI: 10.1007/s00012-022-00779-0
       
  • The number fields that are $${O}^{*}$$ O ∗ -fields

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      Abstract: Abstract Using the theory on infinite primes of fields developed by Harrison in [2], the necessary and sufficient conditions are proved for real number fields to be \(O^{*}\) -fields, and many examples of \(O^{*}\) -fields are provided.
      PubDate: 2022-06-27
      DOI: 10.1007/s00012-022-00781-6
       
  • Divisibility on certain o-groups of matrices

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      Abstract: Abstract We construct non-abelian totally ordered groups of matrices of finite Archimedean rank using the group of o-automorphisms of direct sums of copies of the reals ordered anti-lexicographically. We also prove that each of these o-groups is divisible, and provide, for every \(n>2\) , a specific formula to find the n-th root of every element of such group. Finally, we construct an example of a non-commutative totally ordered ring.
      PubDate: 2022-06-25
      DOI: 10.1007/s00012-022-00778-1
       
 
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