This work clarifies the relationship between the openness of the regular locus of a
commutative Noetherian ring R and the existence of generators for the category of finitely …

Let R be a commutative Noetherian local ring with residue field k. Let X be a resolving
subcategory of finitely generated R-modules. This paper mainly studies when X contains k …

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 …

The cohomology annihilator of a noetherian ring that is finitely generated as a module over
its center is introduced. Results are established linking the existence of nontrivial …

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 …

Let $ A $ be a commutative noetherian ring. In this paper, we interpret localizing
subcategories of the derived category of $ A $ by using subsets of Spec $ A $ and …

Let $ R $ be a commutative noetherian ring. Denote by $\operatorname {mod} R $ the
category of finitely generated $ R $-modules, by $\operatorname {D^ b}(R) $ the bounded …

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 …

Let R be a commutative noetherian local ring, and let 𝒳 be a resolving subcategory of the
category of finitely generated R-modules. In this paper, we study modules in 𝒳 by relating …

Firstly, we compare the bounded derived categories with respect to the pure-exact and the
usual exact structures, and describe bounded derived category by pure-projective modules …