Abstract:
A commutative ring $R$ is called feebly invo-clean if any its element is of the form $\nu+e-f$, where $\nu$ is an involution and $e$, $f$ are idempotents. For every commutative unital ring $R$ and every abelian group $G$ we find a necessary and sufficient condition only in terms of $R$, $G$ and their sections when the group ring $R[G]$ is feebly invo-clean. Our result improves two recent own achievements about commutative invo-clean and weakly invo-clean group rings, published in Univ. J. Math. & Math. Sci. (2018) and Ural Math. J. (2019), respectively.
Keywords:invo-clean rings, weakly invo-clean rings, feebly invo-clean rings, group rings.
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