Let R be a commutative noetherian ring. In this paper, we find out close relationships
between the module M being embedded in a module of projective dimension at most n and …

While the notions of Baer, quasi-Baer and extending modules are related to each other, it is
well known that these are distinct notions in general. In this paper, we investigate a number …

Let R be a commutative Noetherian ring, a be an ideal of R and M be a finitely generated R-
module. Melkersson and Schenzel asked whether the set\rm Ass _R\rm Ext^ i_R (R/a^ j, M) …

Dans la conférence qu'il a donnée au Colloque de Bruxelles, en 1956, M. Paul DUBREIL a
caractérisé les anneaux, commutatifs, unitaires, dont le treillis des idéaux est totalement …

Let $\mathcal {S} $ be a class of finitely presented $ R $-modules such that $ R\in\mathcal
{S} $ and $\mathcal {S} $ has a subset $\mathcal {S}^*, $ with the property that for any …

Let R be a ring, and let (ℐ, ℱ) be an hereditary torsion theory of left R-modules. An
epimorphism ψ: M→ X is called a torsion-free cover of X if (1) M∈ ℱ,(2) every …

Let R be a commutative ring and ℱ a Gabriel topology of R. We discuss the R's satisfying the
condition that for all ℱ-torsion R-modules T, T is ℱ-injective if and only if T is locally ℱ …

A module UR is couniform if it has dual Goldie dimension 1, that is, it is non-zero and the
sum of any two proper submodules of UR is a proper submodule of UR. A module MR is …

Let $ R $ be a Noetherian local ring, and let $ C $ be a semidualizing $ R $-module. In this
paper, we present some results concerning to vanishing of $\operatorname {Ext} $ and finite …

Given a finitely generated module $ M $ over a Noetherian local ring $ R $, one would like to
know when the corresponding associated graded module has a pure resolution over $ G …