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Displaying similar documents to “On some commutativity theorems for finite rings and finite groups”

G -nilpotent units of commutative group rings

Peter Vassilev Danchev (2012)

Commentationes Mathematicae Universitatis Carolinae

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Suppose R is a commutative unital ring and G is an abelian group. We give a general criterion only in terms of R and G when all normalized units in the commutative group ring R G are G -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].

Rings generalized by tripotents and nilpotents

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi (2022)

Czechoslovak Mathematical Journal

Similarity:

We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).