A new generalization of semiregular rings

Abstract

A ring R is called $\nu$-semiregular  if for every semisimple principal right ideal aR of R,  there exists $e^2=e\in aR$  such that $(1-e)a\in J(R)$. The class of right $\nu$-semiregular rings contains all semiregular rings. Some properties of these rings are studied and some results about semiregular rings are extended.