Weakly quasi invo-clean rings

Abstract

We introduce the notion of weakly quasi invo-clean rings where every element $ r $ can be written as $ r=v+e $ or $ r=v-e $, where $v\in Qinv(R)$ and $ e\in Id(R) $. We study various properties of weakly quasi invo-clean elements and weakly quasi invo-clean rings. We prove that the ring $ R=\prod_{i\in I} R_i $, where all rings $ R_i $ are weakly quasi invo-clean, is weakly quasi invo-clean ring if and only if all factors but one are quasi invo-clean.