Geodesic
Commutative feebly invo-clean group rings
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 61 (2019), pp. 5-10

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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. 
@article{VTGU_2019_61_a0,
     author = {P. V. Danchev},
     title = {Commutative feebly invo-clean group rings},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--10},
     publisher = {mathdoc},
     number = {61},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2019_61_a0/}
}
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P. V. Danchev. Commutative feebly invo-clean group rings. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 61 (2019), pp. 5-10. http://geodesic.mathdoc.fr/item/VTGU_2019_61_a0/