Central quasi-morphicity, central morphicity, and strongly $\pi$-regularity

Abstract

This paper revisits the notions of centrally morphic and centrally quasi-morphic modules introduced by Dehghani and Sedaghatjoo. We identify sufficient conditions under which these notions become equivalent. In particular, if a module \( M \) is image-projective, generates its kernels, and its endomorphism ring has von Neumann regular center, then central morphicity, central quasi-morphicity, and right central morphicity of the endomorphism ring are equivalent. We also prove that centrally morphic rings with von Neumann regular center and ACC on principal right annihilators are strongly \(π\)-regular.

arXiv commentrevised version