Results 11 to 20 of about 219,014 (266)
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
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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
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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
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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
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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
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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
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Commutative periodic group rings
Математичні Студії, 2020 We find a satisfactory criterion when a commutative group ring $R(G)$ is periodic only in terms of $R$, $G$ and their sections, provided that $R$ is local.
P. Danchev
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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 $xx^σ=x^σx$ for all $x=\sum_{g\in G}α_gg\in KG$, where \quad $x\mapsto x^σ=~\sum_{g\in G}α_gf(g)σ(g)$\quad is an involution of $KG$; here $f: G\to U(K)$ is a homomorphism and $σ$ is an anti-automorphism of order two of $G$.
BOVDI V, SICILIANO, Salvatore
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COTORSION DIMENSIONS OVER GROUP RINGS [PDF]
Journal of Algebraic Systems, 2019 Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module.
A. Hajizamani
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Group extensions and automorphism group rings [PDF]
Homology, Homotopy and Applications, 2003 The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.
Martino, John, Priddy, Stewart
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