Let cp be a ring homomorphism from a ring R to a ring Q. If Q is flat as a right R-module and
q is a ring epimorphism, we say that QR is a flat epimorphism. If Q is projective with respect …

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to
and irreducible epimorphisms from finitely generated free modules over a noetherian local …

Let R be a commutative ring and M a nonzero R-module. We introduce the class of pseudo-
strongly (PS)-hollow submodules of M. Inspired by the theory of modules with secondary …

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 …

In this paper, we prove that the Bass class with respect to a semidualizing bimodule C
contains all FP-injective S-modules. We introduce the definition of C-FP-injective modules …

Classically, the Auslander–Bridger transpose finds its best applications in the well-known
setting of finitely presented modules over a semiperfect ring. We introduce a class of …

In this paper, we introduce a general form of pseudo-p-injectivity. Let be a right-module
and=(), its endomorphism ring. A right-module is called a generalized-pseudo-Mp-injective …

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

For a left pure semisimple ring R, it is shown that the local duality establishes a bijection
between the preinjective left R-modules and the preprojective right R-modules, and any …

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