Let $ R $ be the quotient of a regular coherent commutative ring by a finitely generated
ideal. In this paper, we classify all abelian subcategories of finitely presented $ R $-modules …

Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal.
Hovey gave a bijection between the set of coherent subcategories of the category of finitely …

For a commutative noetherian ring A, we compare the support of a complex of A-modules
with the support of its cohomology. This leads to a classification of all full subcategories of A …

For R a commutative Noetherian ring, wide and Serre subcategories of finitely generated R-
modules have been classified by their support. This paper studies general torsion classes …

In this note we show that a countable injective module is $\sum $-injective and consequently
a ring $ R $ is left noetherian if the category of left $ R $-modules has a countable injective …

Let f: B→ A be an analytic isomorphism along an element s of B. Then it is shown that the
following square is cartesian, where for a ring RM (R) denotes the category of finitely …

Given a commutative coherent ring $ R $, a bijective correspondence between the thick
subcategories of perfect complexes $\mathcal D_ {\operatorname {per}}(R) $ and the Serre …

Let $ R $ denote a commutative Noetherian (not necessarily local) ring and $ I $ an ideal of
$ R $ of dimension one. The main purpose of this paper is to generalize, and to provide a …

A module is said to be copure injective if it is injective with respect to all modules A⊂ B with
B/A injective. We first characterize submodules that have the extension property with respect …

The main results of this paper concern decompositions of an injective module, either as a
direct sum of submodules or as the injective envelope of a direct sum of injective …