Let R be a commutative ring and let P be an NFG (non-finitely generated) projective R-
module. What conditions on R ensure that P is free or at least the direct sum of finitely …

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 …

Publisher Summary This chapter describes the hereditarily and cohereditarily projective
modules. There is a similarity between the study of n-firs and that of right semihereditary …

A ring R is said to be left pure-hereditary (resp. RD-hereditary) if every left ideal of R is pure-
projective (resp. RD-projective). In this paper, some properties and examples of these rings …

Let $ R $ be a ring and $ M $ a right $ R $-module. Let $ N $ be a proper submodule of $ M
$. We say that $ M $ is $ N $-coretractable (or $ M $ is coretractable relative to $ N $) …

Let R be a ring and τ a hereditary torsion theory for the category of all left R-modules. A right
R-module M is called τ-flat if Tor 1 (M, R/I)= 0 for any τ-finitely presented left ideal I. A left R …

We study coherence properties of a module M over its endomorphism ring. Hereby we
extend to modules known characterizations of coherent and π-coherent rings. Moreover, we …

In this paper, we introduce a new generalization of coherent rings. Let m be a positive
integer and da positive integer or d=∞. A ring R is called a left (m, d)-coherent ring in case …

A module M is called pseudo-projective if every epimorphism from M to each quotient
module of M can be lifted to an endomorphism of M. In this paper, we study some properties …

We studied almost relative projective modules and almost relative injective modules in [3, 6,
7]. In this short note we define a new module, an almost projective (resp. almost injective) …