COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS

Peter V. Danchev     (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria)

Abstract


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 necessary and sufficient condition when the group ring \(R[G]\) is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings.


Keywords


Invo-clean rings, Weakly invo-clean rings, Group rings

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References


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DOI: http://dx.doi.org/10.15826/umj.2019.1.005

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