Results 11 to 20 of about 861,658 (327)
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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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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Traces on Semigroup Rings and Leavitt Path Algebras [PDF]
, 2015 The trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators.
Mesyan, Zachary, Vas, Lia
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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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Outer partial actions and partial skew group rings [PDF]
, 2014 We extend the classicial notion of an outer action $\alpha$ of a group $G$ on a unital ring $A$ to the case when $\alpha$ is a partial action on ideals, all of which have local units.
Nystedt, Patrik, Öinert, Johan
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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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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 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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