Results 11 to 20 of about 222,859 (215)
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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Representations of group rings and groups [PDF]
International Journal of Group Theory, 2018 An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. It is shown that for any group ring matrix $A$ of $mathbb{C} G$ there exists a matrix $U$ (independent of $A$) such that $U^{-1}AU= diag(
Ted Hurley
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Journal of Algebra, 2004 An associative ring \(R\) with identity is said to be reversible if \(ab=0\) implies \(ba=0\) for all \(a,b\in R\). The main problem of this paper is the question when the group ring \(K[G]\) of a group \(G\) over a field \(K\) is reversible. The authors prove that if \(G\) is a non-Abelian torsion group and \(K[G]\) is reversible, then \(G\) is ...
Gutan, Marin, Kisielewicz, Andrzej
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Normality in group rings [PDF]
St. Petersburg Mathematical Journal, 2008 8 ...
BOVDI V, SICILIANO, Salvatore
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Journal of Pure and Applied Algebra, 2007 A ring \(R\) is said to be (i) `duo' if every one-sided ideal is two-sided, and (ii) `reversible' if whenever \(\alpha\beta=0\) for \(\alpha,\beta\in R\), then \(\beta\alpha=0\). The main result of this paper states that, for the group algebra \(KG\) of a torsion group \(G\) over a field \(K\), these two properties are equivalent.
Bell, Howard E., Li, Yuanlin
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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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COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS
Ural Mathematical Journal, 2019 A ring \(R\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \(R\) and each abelian group \(G\), we find only in terms of \(R\), \(G\) and their sections a ...
Peter V. Danchev
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On some commutative invariants of modules over minimax nilpotent groups
Доповiдi Нацiональної академiї наук України, 2022 In the paper we introduce a finite system of invariants for modules over minimax nilpotent groups which consists of classes of equivalent prime ideals of the group algebra of an Abelian minimax group. In particuly, introduced system of invariants allows
A.V. Tushev
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On the probability of zero divisor elements in group rings [PDF]
International Journal of Group Theory, 2022 Let $R$ be a non trivial finite commutative ring with identity and $G$ be a non trivial group. We denote by $P(RG)$ the probability that the product of two randomly chosen elements of a finite group ring $RG$ is zero. We show that $P(RG)
Haval Mohammed Salih
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