Commutative Weakly Invo–Clean Group Rings

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.