Kasch modules and pV-rings

Abstract

Let R be a ring. A right R-module M is called p-injective if every homomorphism from a principal right ideal of R to M can be given by a left multiplication. A ring R is called a right pV-ring if every simple R-module is p-injective. In this paper, Kasch modules are considered. It is proved that if a Kasch module M is finitely generated and quasi-p-injective, then there is a bijective correspondence between the class of maximal submodules of M and the class of all minimal left ideals of its endomorphism ring. Also, it is proved that if M is a pV-module which is a finitely generated projective self-generator, then its endomorphism ring is a right pV-ring. Finally, it is proved that being a right or left pV-ring is a Morita, invariant. © 2005 AMSS CAS & Suzhou Univ.