Weakening the notion of R-projectivity, a right R-module M is called max-projective provided
that each homomorphism f: M→ R/I, where I is any maximal right ideal, factors through the …

Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …

Given an R-module C and a class of R-modules 𝒟 over a commutative ring R, we investigate
the relationship between the existence of 𝒟-envelopes (respectively, 𝒟-covers) and the …

We introduce the notion of I-lifting modules as a proper generalization of the notion of lifting
modules and present some properties of this class of modules. It is shown that if M is an I …

Projectivity classes, which dualize injectivity classes (cf.[ll]), are introduced and some
examples are given. Characterizations of hereditary rings, semisimple rings, Noetherian …

In this paper, the" relative" version of semi-projectivity is considered. Let M and N be
modules. N is called M-semi-projective, if any homomorphism from N to an M-cyclic …

The modules which are isomorphic to their non-zero submodules are known as iso-
retractable. We characterize simple modules in terms of iso-retractable modules. We provide …

Abstract A right R-module M is called semi-projective if, for any submodule N of M, every
epimorphism\pi: M\rightarrow N and every homomorphism\alpha: M\rightarrow N, there …

Endomorphism rings and the category of finitely generated projective modules Page 1
COMMLTNICATIONS IN ALGEBRA, 28(8), 3837-3 852 (2000) Endomorphism rings and the …

A module M is called N-almost-invariant for a module N if, for any homomorphism α: F→ E,
either α (N)⊆ M, or there exist nonzero direct summands F′ of F and E′ of E such that α …