Weakly $I$-Semiregular Rings and $I$-Semiregular Rings

Abstract

Let $I$ be an ideal of a ring $R$. We call $R$ weakly $I$-semiregular if $R$/$I$ is a von Neumann regular ring. This definition generalizes $I$-semiregular rings. We give a series of characterizations and properties of this class of rings. Moreover, we also give some properties of $I$-semiregular rings.