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 …

In Faith [Grundlehren der Mathematischen Wissenschaften. 191 (1976)], Faith asked for
what rings $ R $ does the Dual Baer Criterion hold in Mod-$ R $, that is, when does $ R …

Abstract Baer's Criterion for Injectivity is a useful tool of the theory of modules. Its dual
version (DBC) is known to hold for all right perfect rings, but its validity for the non-right …

We apply set-theoretic methods to study projective modules and their generalizations over
transfinite extensions of simple artinian rings R. We prove that if R is small, then the Weak …

Recently, the rings whose injective right modules are R-projective (respectively, max-
projective) were investigated and studied in [2]. Such ring are called right almost-QF …

A right $ R $-module $ M $ is called $ R $-projective provided that it is projective relative to
the right $ R $-module $ R_ {R} $. This paper deals with the rings whose all nonsingular …

A module over a ring R is R-projective if it is projective relative to R. This module-theoretic
notion is dual to the notion of an R-injective module that plays a key role in the classic Baer's …

All rings in this work are right ring and all modules is right module (mod) X over a ring R. A
mod X is said to be nearly maximal projective (for short; Ner. Mx. Pro. Mod)) if∀ …

Abstract A right R-module M is called R-projective provided that it is projective relative to the
right R-module R R. One of the parts of this thesis deals with the rings whose all nonsingular …

Let R be a ring with an identity. A right R-module is said to be R-projective if every
homomorphism from M to R/I can be lifted to a homomorphism from M to R, for each right …