2016
DOI: 10.1142/s0219498817501353
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Nil-clean group rings

Abstract: An element [Formula: see text] of a ring [Formula: see text] is nil-clean, if [Formula: see text], where [Formula: see text] and [Formula: see text] is a nilpotent element, and the ring [Formula: see text] is called nil-clean if each of its elements is nil-clean. In [W. Wm. McGovern, S. Raja and A. Sharp, Commutative nil clean group rings, J. Algebra Appl. 14(6) (2015) 5; Article ID: 1550094], it was proved that, for a commutative ring [Formula: see text] and an abelian group [Formula: see text], the group rin… Show more

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Cited by 17 publications
(12 citation statements)
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“…As told in the previous section, we extend some results from [30] to the graded case. In order to do that, we recall a way to make a group ring graded.…”
Section: Preliminariesmentioning
confidence: 54%
“…As told in the previous section, we extend some results from [30] to the graded case. In order to do that, we recall a way to make a group ring graded.…”
Section: Preliminariesmentioning
confidence: 54%
“…(1) nil(A So by [24,Lemma 2.4], (a, f (a) + k) is strongly nil-clean. Thus C(A ◃▹ f K) is strongly nil-clean.…”
Section: Clean Like Properties Of Amalgamated Ringsmentioning
confidence: 99%
“…Moreover, the strong nilcleanness of Morita contexts, formal matrix rings and generalized matrix rings has also been studied [2]. Noting that semigroup rings are also an extension of group rings, the strong nil-cleanness of certain kinds of group rings has been studied in [2,4,5].…”
Section: Introductionmentioning
confidence: 99%