Finitely hollow-lifting modules

Abstract EN

Let R be any ring and let M be any leftR-module.

We say that M is called a finitely hollow-lifting module (or briefly f-hollow lifting) if every finitely generated sub module N of M with M / N hollow, has a coessential sub module in M that is a direct summand of M.

The main purpose of this paper is to develop the properties of f-hollow-lifting modules.

Also we study the relation between the projectivity and f-hollow-lifting modules.

We prove that for a projective module P, P is f-hollow-lifting module if and only if for every sub module A of p with P / A is hollow, P / A has a protective cover.