Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Journal Prestige (SJR): 0.339 Number of Followers: 2 Partially Free Journal ISSN (Print) 01384821  ISSN (Online) 21910383 Published by SpringerVerlag [2468 journals] 
 On homogeneous $$\eta $$ Einstein almost cosymplectic manifolds

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Abstract: Abstract We prove that every compact, homogeneous \(\eta \) Einstein almost cosymplectic manifold is a cosymplectic manifold.
PubDate: 20240901

 Amalgamated algebra along an ideal defined by Snoetherian
spectrumlikeconditions
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Abstract: Abstract Let \(f:A\longrightarrow B\) be a ring homomorphism and J be an ideal of B. The subring \(A\bowtie ^{f}J:=\{(a,f(a)+j)/ a\in A\quad \text {et}\quad j\in J\}\) of \(A\times B\) is called the amalgamation of A with B along with J with respect to f. In this paper we investigate a general concept of ring with Noetherian spectrum, called SNoetherian spectrum property which was introduced by Hamed, on the \(A\bowtie ^{f}J\) for a multiplicative subset S of \(A\bowtie ^{f}J.\)
PubDate: 20240901

 3absorbing ideals and submodules over noncommutative rings

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Abstract: Abstract Let R be a noncommutative ring with identity. This paper mainly defines the concept of a 3absorbing ideal and submodule. It shows that in the case where the ring is commutative, then these notions concide with the one defined by Badawi and Darani. Further, we give an example to show that in general these notions are different and present some properties of 3absorbing ideals and submodules.
PubDate: 20240901

 On starconvex bodies with rotationally invariant sections

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Abstract: Abstract We will prove that an originsymmetric starconvex body K with sufficiently smooth boundary and such that every hyperplane section of K passing through the origin is a body of affine revolution, is itself a body of affine revolution. This will give a positive answer to the recent question asked by Bor, HernándezLamoneda, Jiménez de Santiago, and MontejanoPeimbert, though with slightly different prerequisites.
PubDate: 20240901

 Discrete asymptotic nets with constant affine mean curvature

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Abstract: Abstract In this paper we define the class of constant affine mean curvature (CAMC) discrete asymptotic nets, which contains the wellknown classes of affine spheres and affine minimal asymptotic nets. This class is defined by considering fields of compatible interpolating quadrics, i.e., quadrics that have common tangent planes at the edges of the net. We show that, for CAMC asymptotic nets, ruled discrete asymptotic nets is equivalent to ruled compatible interpolating quadrics. Moreover, we prove discrete counterparts of some known properties of the Demoulin transform of a smooth CAMC surface.
PubDate: 20240901

 On pseudoHermitian quadratic nilpotent lie algebras

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Abstract: Abstract We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudoHermitian for the given complex structure. We propose several methods to construct such Lie algebras and describe a method of double extension by planes to get an inductive description of all of them. As an application, we give a complete classification of nilpotent quadratic Lie algebras where the metric is LorentzHermitian and we fully classify all nilpotent pseudoHermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudoHermitian metrics.
PubDate: 20240901

 Exploring virtual versions of Hsupplemented and NSmodules

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Abstract: Abstract In this work we introduce virtual versions of Hsupplemented modules and NSmodules. These modules are defined by replacing the condition of being a “direct summand” with being “isomorphic to a direct summand”. The paper explores various equivalent conditions for a module to be virtually Hsupplemented and investigates their fundamental properties. It is discovered that over a right Vring for a module, the concepts virtually Hsupplemented, virtually semisimple and VNS, coincide. Additionally, it is proven that each right Rmodule is VNS if and only if every noncosingular right Rmodule is injective.
PubDate: 20240901

 Braid monodromy and Alexander polynomials of real plane curves

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Abstract: Abstract We describe symmetries of the braid monodromy decomposition for a class of plane curves defined over reals including the real curves with no real points and proving new divisibility relations for Alexander invariants of such curves.
PubDate: 20240901

 Tropical lifting problem for the intersection of plane curves

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Abstract: Abstract Given a tropical divisor D in the intersection of two tropical plane curves, we study when it can be realized as the tropicalization of the intersection of two algebraic curves, and give a sufficient condition. It is shown that under a certain condition involving a graph determined by these tropical curves, we can algorithmically find algebraic curves such that the tropicalization of their intersection is D.
PubDate: 20240901

 Invariant rectification of nonsmooth planar curves

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Abstract: Abstract We consider the problem of defining arc length for a plane curve invariant under a group action. Initially one partitions the curve and sums a distance function applied to consecutive support elements. Arc length then is defined as a limit of approximating distance function sums. Alternatively, arc length is defined using the integral that arises when applying the method to smooth curves. That these definitions agree in the general case for the Euclidean group was an early victory of the Lebesgue integral; the equivalence also is known for the equiaffine group. Here we present a unified treatment for equiaffine, Laguerre, inversive, and Minkowski (pseudoarc) geometries. These are alike in that arc length corresponds with a geometric average of finite Borel measures.
PubDate: 20240901

 The homogeneous spectrum of a $$\mathbb Z_2$$ graded commutative ring

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Abstract: Abstract Let \(\mathbb Z_2:=\mathbb Z/2\mathbb Z\) be the additive group with two elements. In this article, we focus only on \(\mathbb Z_2\) graded commutative ring i.e commutative ring R such that \(R=R_0\oplus R_1\) as Abelian group and \(R_iR_j\subseteq R_{i+j}\) for all \(i,j\in \mathbb Z_2\) . Our main goal is to establish a strong relation between \(\mathbb Z_2\) graded prime (resp., maximal) ideals of R and prime (resp., maximal) ideals of \(R_0\) , for instance, it is showed that, the \(\mathbb Z_2\) graded prime spectrum of R is homeomorphic to the prime spectrum of \(R_0\) with respect to the Zariski topologies.
PubDate: 20240901

 Packing of nonblocking cubes into the unit cube

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Abstract: Abstract Any collection of nonblocking cubes, whose total volume does not exceed 1/3, can be packed into the unit cube.
PubDate: 20240901

 Generalized derivations with nilpotent values on Lie ideals in semiprime
rings
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Abstract: Abstract Let R be a prime ring of characteristic different from 2, \(Q_r\) its right Martindale quotient ring, C its extended centroid, L a noncentral Lie ideal of R, \(n\ge 1\) a fixed integer, F and G two generalized derivations of R. If \(\bigl (F(xy)G(x)G(y)\bigr )^n=0\) , for any \(x,y \in L\) , then there exists \(\lambda \in C\) such that \(F(x)=\lambda ^2 x\) and \(G(x)=\lambda x\) , for any \(x\in R\) . Moreover, we analyze the semiprime case.
PubDate: 20240901

 Extended dot product graph of a commutative ring

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Abstract: Abstract Let B be a commutative ring with \(1\ne 0\) , \(1\le m <\infty \) be an integer and \(R=B\times B\times \cdots \times B\) (m times). The extended total dot product graph \(\overline{TD}(R)\) and extended zerodivisor dot product graph \(\overline{ZD}(R)\) are undirected graphs with vertex sets \(R^{*} = R{\setminus }\{(0,0,\ldots 0)\}\) and \(Z^{*}(R)=Z(R){\setminus }\{(0,0,\ldots 0)\}\) respectively. Two distinct vertices \(a=(a_1,a_2,\ldots ,a_m)\) and \(b=(b_1,b_2,\ldots ,b_m)\) are adjacent in \(\overline{TD}(R)\) and \(\overline{ZD}(R)\) if there exist positive integers k and \(\ell \) such that \(a^k\cdot b^\ell =0\) with \(a^k\ne 0\) and \(b^\ell \ne 0\) respectively (where \(a^k\cdot b^\ell =a_1^kb_1^\ell +a_2^kb_2^\ell +\cdot \cdot \cdot +a_m^kb_m^\ell \in B\) , denotes the normal dot product of \(a^k\) and \(b^\ell \) ). In this paper, we study about connectedness, diameter and girth of \(\overline{TD}(R)\) and \(\overline{ZD}(R)\) . We also characterize all rings R for which \(\overline{TD}(R)\) and \(\overline{ZD}(R)\) are planar and outerplanar.
PubDate: 20240901

 On the classification of nonaCM curves on quintic surfaces in $$\mathbb
{P}^3$$
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Abstract: Abstract In this paper, a curve is any projective scheme of pure dimension one. It is well known that the arithmetic genus and the degree of an aCM curve D in \(\mathbb {P}^3\) are computed by the hvector of D. However, for a given curve D in \(\mathbb {P}^3\) , the two aforementioned invariants of D do not tell us whether D is aCM or not. If D is an aCM curve on a smooth surface X in \(\mathbb {P}^3\) , any member of the linear system \( D+lC \) is also aCM for each nonnegative integer l, where C is a hyperplane section of X. By a previous work, if a nonzero effective divisor D of degree d and arithmetic genus g on a smooth quintic surface X in \(\mathbb {P}^3\) is aCM and satisfies the condition \(h^0(\mathcal {O}_X(DC))=0\) , then \(0\le d+1g\le 4\) . In this paper, we classify nonaCM effective divisors on smooth quintic surfaces in \(\mathbb {P}^3\) of degree d and arithmetic genus g such that \(0\le d+1g\le 4\) , and give several examples of them.
PubDate: 20240901

 Gaps on the intersection numbers of sections on a rational elliptic
surface
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Abstract: Abstract Given a rational elliptic surface X over an algebraically closed field, we investigate whether a given natural number k can be the intersection number of two sections of X. If not, we say that k is a gap number. We try to answer when gap numbers exist, how they are distributed and how to identify them. Our main tool is the Mordell–Weil lattice, which connects the investigation to the classical problem of representing integers by positivedefinite quadratic forms.
PubDate: 20240901

 Regularity via links and Stein factorization

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Abstract: Abstract Here, we introduce a new definition of regular point for piecewiselinear (PL) functions on combinatorial (PL triangulated) manifolds. This definition is given in terms of the restriction of the function to the link of the point. We show that our definition of regularity is distinct from other definitions that exist in the combinatorial topology literature. Next, we stratify the Jacobi set/critical locus of such a map as a poset stratified space. As an application, we consider the Reeb space of a PL function, stratify the Reeb space as well as the target of the function, and show that the Stein factorization is a map of stratified spaces.
PubDate: 20240901

 Brauer groups and Picard groups of the moduli of parabolic vector bundles
on a nodal curve
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Abstract: Abstract We determine the Brauer groups and Picard groups of the moduli space \(U^{' s}_{L,par}\) of stable parabolic vector bundles of rank r with determinant L on a complex nodal curve Y of arithmetic genus \(g \ge 2\) . We also compute the Picard group of the moduli stack for parabolic SL(r)bundles on Y and use it to give another description of the Picard group of \(U^{' s}_{L,par}\) . For \(g \ge 2\) , we determine the Brauer group of the moduli space \(U^{' s}_L\) of stable vector bundles on Y of rank r with determinant L, deduce that \(U^{' s}_L\) is simply connected and show the nonexistence of the universal bundle on \(U^{' s}_L \times Y\) in the noncoprime case.
PubDate: 20240901

 Jequivalence for associative algebras

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Abstract: Abstract We study the combinatorics of an analogue of Green’s \({\mathcal {J}}\) relation (a.k.a. the twosided relation) for the bicategory of finitedimensional bimodules over finitedimensional associative algebras over a fixed field. In particular, we provide a number of exameples for both \({\mathcal {J}}\) equivalent and inequivalent but \({\mathcal {J}}\) comparabe algebras.
PubDate: 20240809

 Totally simple modules

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Abstract: Abstract Simple modules on a ring have information about a part of the spectrum (the maximal spectrum) and, in some cases, about the whole ring. Therefore, knowledge about the structure and properties of simple modules is of interest. In the case we are interested in: chain conditions on modules relative to a multiplicative set \(S\subseteq {A}\) or a hereditary torsion theory \(\sigma \) in \({{\,\mathrm{{\textbf {Mod}}}\,}}{A}\) , we find that two different classes of totally simple modules appear. Given a multiplicative subset \(S\subseteq {A}\) one tends to introduce Ssimple modules either as those non totally Storsion which are Sminimal, or as those for which \(0\subseteq {M}\) is Smaximal. Apparently these two definitions are different. We show that both definitions coincide, and define an Amodule M to be Ssimple whenever it satisfies: (1) \({{\,\textrm{Ann}\,}}(M)\cap {S}=\varnothing \) ; (2) there exists \(s\in {S}\) such that \(\sigma _S(M)s=0\) , and (3) \(Ms\subseteq {L}\) , for every no totally Storsion submodule \(L\subseteq {M}\) . The main goal of this paper is to provide examples of this kind of totally simple modules by delving into their structure. As a byproduct we explore the relationship between these totally simple modules and totally prime modules, and the local behaviour of totally simple modules. We complete the paper by providing examples of this theory.
PubDate: 20240806
