Semi-complemented commutative group rings

Abstract

Recall that an element $x\in R$ is {\bf complemented} if there is a $y\in R$ such that $xy = 0$ and $x + y \in {\rm reg}(R)$. In a recent article [1], the authors investigated those rings for which every non-nilpotent element is complemented, calling such rings {\bf semi-complemented}. As the title of the current work suggests we characterize when a commutative group $RG$ is semi-complemented