Communications in Algebra

Chelnokov, Grigory; Mednykh, Alexander

doi: 10.1080/00927872.2019.1705468pmid: N/A

AbstractThere are only 10 Euclidean forms, that is flat closed three-dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of n-fold coverings over orientable Euclidean manifolds and and calculate the numbers of nonequivalent coverings of each type. We classify subgroups in the fundamental groups and up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index n. The manifolds and are uniquely determined among the others orientable forms by their homology groups and

Fine, Benjamin; Gaglione, Anthony M.; Rosenberger, Gerhard; Spellman, Dennis

doi: 10.1080/00927872.2019.1710158pmid: N/A

AbstractWe introduce three first-order languages with equality Ln, n = 0, 1, 2. We list axioms Tn expressed in Ln and view a group as a model of and a ring as a model of T1. Moreover, we view the class of group rings as a subclass of the model class of T2. The paper consists of two parts. In Part (I), we prove that if ] is elementarily equivalent to with respect to L2, then, simultaneously the group G is elementarily equivalent to the group H with respect to L0 and the ring R is elementarily equivalent to the ring S with respect to In Part(II) we let F be a rank 2 free group and be the ring of integers. We show that if G is universally equivalent to F with respect to L0 and R is universally equivalent to with respect to L1, then, is universally equivalent to with respect to L1. Furthermore, we show that, if R is universally equivalent to with respect to L1 and is universally equivalent to with respect to L1, then, G is universally equivalent to F with respect to L0.

Lee, Gangyong; Rizvi, S. Tariq

doi: 10.1080/00927872.2020.1722825pmid: N/A

AbstractThe purpose of this paper is to further the study of quasi-Baer modules by investigating the structure of a special class of quasi-Baer modules. As a module theoretic analog of a piecewise prime ring, we define and characterize a piecewise prime module (simply, a PWP module) via its endomorphism ring. Although it is well known that eRe is a PWP ring for a left (right) semicentral idempotent or a full idempotent e in a PWP ring R, it is still an open question whether this holds true when e is an arbitrary idempotent. We give an affirmative answer to this question. As a consequence, we prove that every direct summand of a PWP module is a PWP module. It is shown that any direct sum of copies of a PWP module is always a PWP module. Consequently, every column (and row) finite matrix ring over a PWP ring is a PWP ring. We obtain a complete structure theorem for PWP modules and show that endoprime submodules are the building blocks of the PWP modules. Applications and examples illustrating our results are provided.

Alawam, Fatin; Bani-Ata, Mashhour

doi: 10.1080/00927872.2020.1722826pmid: N/A

AbstractThe purpose of this article is to give a new, explicit and elementary construction of the in using the notion of M-sets introduced by the second author, and properties of the generalized quadrangle of type This construction is elementary and explicit as the transpositions generating in have been explicitly constructed and implemented in GAP, which might be very helpful and well suited to people who do computations with this group. It is remarkable to mention that this work supports the work of Cuypers et al., where the existence of has been assumed then the embedding of the sporadic simple group in the group has been given. In fact our approach for the construction is completely different from Fischer’s construction.

Chen, Jingshan

doi: 10.1080/00927872.2020.1722827pmid: N/A

AbstractIn this paper, we will give a complete classification of Gorenstein stable log surfaces with where In particular, we classify Gorenstein stable surfaces with

Kemp, Paula; Ratliff, Louis J.; Shah, Kishor

doi: 10.1080/00927872.2020.1722828pmid: N/A

AbstractThis paper contributes several results to the analytic theory of ideals. The main new concept is that of a prereduction (together with the closely related type-prereduction): if R is a ring and I (proper subset) are proper ideals in R, then A is called a prereduction of I in case A is not a reduction of I, but each ideal between A and I is a reduction of I. It is shown that each non-nilpotent proper ideal in a Noetherian ring has at least one prereduction, and a number of the basic properties of the ideals in the set of all prereductions of I are proved. Also, if I is a non-nilpotent proper ideal in a local (Noetherian) ring (R, M), then:There is a natural one-to-one correspondence between the set of the equivalence classes of the type-prereductions of I and the set of the maximal relevant ideals in the Rees ring of I (that is, the homogeneous prime ideals Q in the ring (t an indeterminate) such that and the Krull dimension of is equal to one). is the set of maximal elements in for all positive integers n, and, for each for all large integers m.A complete description is given of the prereductions and the elements in for each ideal I that is generated by analytically independent elements.If R/M is algebraically closed and I is a non-nilpotent and non-principal ideal in R, then there is a natural one-to-one correspondence between the sets and and for all positive integer n.

Ilić-Georgijević, Emil; Şahinkaya, Serap

doi: 10.1080/00927872.2020.1722829pmid: N/A

AbstractWe study the graded isoradical of a ring graded by a group. In particular, we compare the graded isoradical and the classical isoradical of a graded ring, examine the question of how the (graded) isoradical of a graded ring depends on the classical isoradical of a ring which corresponds to the identity element of the grading group, and we also give some sufficient conditions under which the classical isoradical of a graded ring is homogeneous.

Alikhani, Saeid; Ramezani, Fatemeh; Vatandoost, Ebrahim

doi: 10.1080/00927872.2020.1722830pmid: N/A

AbstractA signed dominating function of graph Γ is a function such that for each The signed domination number is the minimum weight of a signed dominating function on Γ. Let be a finite group such that In this paper, we obtain the signed domination number of based on cardinality of S. Also we determine the classification of group G by and

Burns, J. M.; Makrooni, M. A.

doi: 10.1080/00927872.2020.1723020pmid: N/A

AbstractIn this note, we study the subroot system of an irreducible (reduced, crystallographic) root system obtained by taking the orthogonal complement of the highest root. We describe root theoretic data (the Coxeter number and the largest coefficient of the highest root when expressed in terms of the simple roots) of this subroot system in terms of that of As an application, we obtain a new description of the Coxeter exponents of a complex simple Lie algebra.

Aküzüm, Yeşim; Deveci, Ömür

doi: 10.1080/00927872.2020.1723609pmid: N/A

AbstractIn this paper, we give the relationships between the orders of the cyclic groups obtained from the generating matrices of the Hadamard-type k-step Fibonacci sequences and the periods and the ranks of the Hadamard-type k-step Fibonacci sequences modulo m. We also extend the Hadamard-type k-step Fibonacci sequences to groups and then we investigate the structure of groups which have two or three generators by the aid of these sequences. Furthermore, we determine the periods and the ranks of the Hadamard-type k-step Fibonacci sequences in finite groups using the basic Hadamard-type k-step Fibonacci sequences. Finally, we obtain the periods, the basic periods and the ranks of the Hadamard-type 3-step Fibonacci sequences in the dihedral group and the generalized quaternion group with respect to the generating pairs (a, b) and