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 Algebra and Logic   [SJR: 0.566]   [H-I: 18]   [4 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1573-8302 - ISSN (Online) 0002-5232    Published by Springer-Verlag  [2355 journals]
• A Representation of Virtual Braids by Automorphisms
• Authors: V. G. Bardakov; M. V. Neshchadim
Pages: 355 - 361
Abstract: We study a representation of the virtual braid group VBn into the automorphism group of a free product of a free group and a free Abelian group, proposed by S. Kamada. It is proved that the given representation is equivalent to the representation constructed in [http://arxiv.org/abs/1603.01425]; i.e. the kernels of these representations coincide.
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9457-2
Issue No: Vol. 56, No. 5 (2017)

• The Specht Property of L -Varieties of Vector Spaces
• Authors: A. V. Kislitsin
Pages: 362 - 369
Abstract: Conditions are explored which imply the finite basis property for identities of vector spaces embedded in associative algebras over an infinite field. An L-variety having no finite basis of identities, which is the join of two Spechtian L-varieties, is exemplified.
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9458-1
Issue No: Vol. 56, No. 5 (2017)

• Strong Decidability and Strong Recognizability
• Authors: L. L. Maksimova; V. F. Yun
Pages: 370 - 385
Abstract: Extensions of Johansson’s minimal logic J are considered. It is proved that families of negative and nontrivial logics and a series of other families are strongly decidable over J. This means that, given any finite list Rul of axiom schemes and rules of inference, we can effectively verify whether the logic with axioms and schemes, J + Rul, belongs to a given family. Strong recognizability over J is proved for known logics Neg, Gl, and KC as well as for logics LC and NC and all their extensions.
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9459-0
Issue No: Vol. 56, No. 5 (2017)

• Hyperidentities of Quasilinear Clones Containing Creative Functions
• Authors: I. A. Mal’tsev
Pages: 386 - 394
Abstract: We consider the possibility for separating by hyperidentities clones of quasilinear functions defined on the set {0, 1, 2} with values in the set {0, 1}. It is proved that every creative clone of this kind can be separated by a hyperidentity from any noncreative clone comparable with it.
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9460-7
Issue No: Vol. 56, No. 5 (2017)

• Divisible Rigid Groups. Algebraic Closedness and Elementary Theory
• Authors: N. S. Romanovskii
Pages: 395 - 408
Abstract: A group G is said to be rigid if it contains a normal series G = G 1 > G 2 > … > Gm > G m+1 = 1, whose quotients G i/G i+1 are Abelian and, treated as right ℤ[G/G i ]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient G i /G i+1 are divisible by nonzero elements of the ring ℤ[G/G i ]. Every rigid group is embedded in a divisible one. We prove two theorems. Theorem 1 says that the following three conditions for a group G are equivalent: G is algebraically closed in the class Σ m of all m-rigid groups; G is existentially closed in the class Σ m ; G is a divisible m-rigid group. Theorem 2 states that the elementary theory of a class of divisible m-rigid groups is complete.
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9461-6
Issue No: Vol. 56, No. 5 (2017)

• Decompositions in Complete Lattices III. Unique Irredundant Decompositions
and Convex Geometries
• Authors: M. V. Schwidefsky
Pages: 409 - 424
Abstract: We give a characterization of complete strongly dually atomic lattices having unique irredundant decompositions which are also canonical. It is shown that all known characterizations of lattices with unique irredundant decompositions are a consequence of this result. In addition, upper continuous closure lattices of convex geometries with (unique) irredundant decompositions are characterized.
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9462-5
Issue No: Vol. 56, No. 5 (2017)

• A Computable Structure with Nonstandard Computability
• Authors: R. R. Avdeev; V. G. Puzarenko
Pages: 425 - 426
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9463-4
Issue No: Vol. 56, No. 5 (2017)

• Molien–Wedderburn Theorem for Associative Conformal Algebras with Finite
Faithful Representation
• Authors: P. S. Kolesnikov; R. A. Kozlov
Pages: 427 - 428
PubDate: 2017-11-01
DOI: 10.1007/s10469-017-9464-3
Issue No: Vol. 56, No. 5 (2017)

• Sessions of the Seminar “Algebra i Logika”
• PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9456-3

• Fragments of Functional Clones
• Authors: A. G. Pinus
Abstract: In [1] we came up with some approach and problems associated with subsets of functional clones on a fixed set that consist of functions occurring in a clone with a fixed restriction on their arity. This approach receives further development.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9452-7

• P -Stable Polygons
• Authors: A. A. Stepanova; D. O. Ptakhov
Abstract: P-stable polygons are studied. It is proved that the property of being (P, s)-, (P, a)-, and (P, e)-stable for the class of all polygons over a monoid S is equivalent to S being a group. We describe the structure of (P, s)-, (P, a)-, and (P, e)-stable polygons SA over a countable left zero monoid S and, under the condition that the set A \ SA is indiscernible, over a right zero monoid.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9453-6

• Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence
• Authors: E. Yu. Daniyarova; A. G. Myasnikov; V. N. Remeslennikov
Abstract: The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures $$\mathcal{A}$$ and ℬ of a language L, the classification problems for algebraic sets over $$\mathcal{A}$$ and ℬ are equivalent. We establish a connection between geometrical equivalence and quasiequational equivalence.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9449-2

• Reducibility of Computable Metrics on the Real Line
• Authors: R. A. Kornev
Abstract: We study computable reducibility of computable metrics on R induced by reducibility of their respective Cauchy representations. It is proved that this ordering has a subordering isomorphic to an arbitrary countable tree. Also we introduce a weak version of computable reducibility and construct a countable antichain of computable metrics that are incomparable with respect to it. Informally, copies of the real line equipped with these metrics are pairwise homeomorphic but not computably homeomorphic.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9451-8

• Automorphism Groups of Small Distance-Regular Graphs
• Authors: I. N. Belousov; A. A. Makhnev
Abstract: We consider undirected graphs without loops and multiple edges. Previously, V. P. Burichenko and A. A. Makhnev [1] found intersection arrays of distance-regular locally cyclic graphs with the number of vertices at most 1000. It is shown that the automorphism group of a graph with intersection array {15, 12, 1; 1, 2, 15}, {35, 32, 1; 1, 2, 35}, {39, 36, 1; 1, 2, 39}, or {42, 39, 1; 1, 3, 42} (such a graph enters the above-mentioned list) acts intransitively on the set of its vertices.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9447-4

• Universal Generalized Computable Numberings and Hyperimmunity
• Authors: M. Kh. Faizrakhmanov
Abstract: Generalized computable numberings relative to hyperimmune and high oracles are studied. We give a description of oracles relative to which every finite computable family has a universal computable numbering. Also we present a characterization of the class of oracles relative to which every universal computable numbering of an arbitrary finite family is precomplete, and establish a sufficient condition for universal generalized computable numberings to be precomplete. In addition, we look into the question on limitedness of universal numberings computable relative to high oracles.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9454-5

• Automorphism Groups of Diagonal Z p -Forms of the Lie Algebra sl 2 ( Q p
), p &gt; 2
• Authors: A. N. Grishkov; M. N. Rasskazova
Abstract: It follows from [2] that two nondiagonal forms like S(n, d) + Z p A and S(n, d) + Z p A ′ are isomorphic if the elements of A and A′ are conjugated via the group $${\mathrm{Aut}}_{{\boldsymbol{Z}}_p}S\left(n,d\right)$$ . In the present paper, we settle just this question on conjugation. In other words, we describe the group $${\mathrm{Aut}}_{{\boldsymbol{Z}}_p}S\left(n,d\right)$$ and clarify under which conditions two elements of S(n, d) are conjugate under the action of this group on S(n, d), p > 2.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9448-3

• Elementary Equivalence of Partially Commutative Lie Rings and Algebras
• Authors: E. N. Poroshenko
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9455-4

• Solimit Points and u -Extensions
• Authors: Yu. L. Ershov
Abstract: We give a characterization of u-extensions of topological T0-spaces and also of sober spaces using a new concept of a solimit point. It is shown that the sobrification of an arbitrary T0-space coincides with its greatest u-extension.
PubDate: 2017-11-07
DOI: 10.1007/s10469-017-9450-9

• Sessions of the Seminar “Algebra i Logika”
• PubDate: 2017-10-05
DOI: 10.1007/s10469-017-9446-5

• The Isomorphism Problem for Generalized Baumslag–Solitar Groups with
One Mobile Edge
• Authors: F. A. Dudkin
Abstract: A generalized Baumslag–Solitar group (GBS group) is a finitely generated group G which acts on a tree with all edge and vertex stabilizers infinite cyclic. Every GBS group is the fundamental group π1(ð”¸) of some labeled graph ð”¸. This paper deals with the isomorphism problem for GBS groups, which is the problem of determining whether π1(ð”¸) ≅ π1(ð”¹) for two given labeled graphs ð”¸ and ð”¹. We describe an algorithm that decides this problem for the case where one of the labeled graphs has a sole mobile edge.
PubDate: 2017-10-05
DOI: 10.1007/s10469-017-9440-y

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