Endomorphism rings and formal matrix rings of pseudo-projective modules

Abstract

A module M is called pseudo-projective if every epimorphism from M to each quotient module of M can be lifted to an endomorphism of M. In this paper, we study some properties of pseudo-projective modules and their endomorphism rings. It shows that if M is a self-cogenerator pseudo-projective module with finite hollow dimension, End(M) is a semilocal ring and every maximal right ideal of End(M) has of the form {s ? End(M)| Im(s) + Ker(h) ? M} for some endomorphism h of M with h(M) hollow. Moreover, it shows that a pseudo-projective R-module Mis an SSP-module if and only if the product of any two regular elements of End(M) is a regular element. Finally, we investigate the pseudo-projectivity of modules over a formal triangular matrix ring.