Results 1 to 10 of about 861,658 (327)
Normality in group rings [PDF]
St. Petersburg Mathematical Journal, 2008 Let $KG$ be the group ring of a group $G$ over a commutative ring $K$ with unity. The rings $KG$ are described for which $xx^\sigma=x^\sigma x$ for all $x=\sum_{g\in G}\alpha_gg\in KG$, where \quad $x\mapsto x^\sigma=~\sum_{g\in G}\alpha_gf(g)\sigma(g ...
Bovdi, V. A., Siciliano, S.
core +5 more sources
Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings [PDF]
Cubo, 2012 Let R be a commutative unitary ring of prime characteristic p which is a direct product of indecomposable subrings and let G be a multiplicative Abelian group such that G0/Gp is nite.
Peter Danchev
doaj +2 more sources
Proceedings of the American Mathematical Society, 1957 Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M.
Maurice Auslander
openalex +3 more sources
NeutroAlgebra of Idempotents in Group Rings [PDF]
Neutrosophic Sets and Systems, 2022 In this paper, the authors study the new concept of NeutroAlgebra of idempotents in group rings. It is assumed that RG is the group ring of a group G over the ring R. R should be a commutative ring with unit 1.
Vasantha Kandasamy +1 more
doaj +1 more source
Secure Group Communications Using Twisted Group Rings
Mathematics, 2022 In this paper we introduce a Group Key Management protocol following the idea of the classical protocol that extends the well-known Diffie–Hellman key agreement to a group of users. The protocol is defined in a non-commutative setting, more precisely, in
María Dolores Gómez Olvera +2 more
doaj +1 more source
The Axiomatics of Free Group Rings [PDF]
Groups, Complexity, Cryptology, 2021 In [FGRS1,FGRS2] the relationship between the universal and elementary theory of a group ring $R[G]$ and the corresponding universal and elementary theory of the associated group $G$ and ring $R$ was examined.
Benjamin Fine +4 more
doaj +1 more source
Proceedings of the American Mathematical Society, 1972 Two theorems showing the existence of primitive group rings are proved. THEOREM 1. Let G be a countable locally finite group and F a field of characteristic 0, or characteristic p if G has no elements of' order p. Then the group ring F[G] is primitive if and only if G has no finite normal subgroups. THEOREM 2. Let G be any grolp, and F afield.
Formanek, Edward, Snider, Robert L.
openaire +2 more sources
On the structure of groups admitting faithful modules with certain conditions of primitivity
Researches in Mathematics, 2023 In the paper we study structure of soluble-by-finite groups of finite torsion-free rank which admit faithful modules with conditions of primitivity. In particular, we prove that under some additional conditions if an infinite finitely generated linear ...
A.V. Tushev
doaj +1 more source
Zero Insertive Group Rings [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعية, 2008 The aim of this research is to find the necessary and sufficient conditions on a ring A and a group G for which the group ring A[G] to be a zero inserted ring (zi-ring), a zero commutative ring (zc-ring), and a duo- ring. In this paper, we found that the
Amani Sbeih
doaj +1 more source
On invariant ideals in group rings of torsion-free minimax nilpotent groups
Researches in Mathematics, 2023 Let $k$ be a field and let $N$ be a nilpotent minimax torsion-free group acted by a solvable group of operators $G$ of finite rank. In the presented paper we study properties of some types of $G$-invariant ideals of the group ring $kN$.
A.V. Tushev
doaj +1 more source