Max-projective modules

Abstract

A right R-module M is called max-projective provided that each homomorphism ϕ : M → R/I where I is any maximal right ideal,factors through the canonical projection ψ : R → R/I.We call a ring R right GV -ring if all simple singular right R-module are either injective or projective.This thesis attempts to understand the property of max-projective modules over a rings.Among other results we prove that,Over right GV -rings every module is max-projective modules.When we prove weather a direct sum of max-projective modules is max-projective or not, the final result is max-projective modules.Therefore,the direct sum of max-projective modules is max-projective modules.Over right hereditary right noetherian rings,semiperfect rings and right nonsingular right self injective rings, every finitely generated max-projective right modules are projective,and also we prove that over right max-testing rings, every max-projective modules are projective.