We introduce a new notion of commutative noetherian local rings, which we call dominant.
We explore fundamental properties of dominant local rings and compare them with other …

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, 𝔪) be a commutative noetherian local ring. In this paper, we prove that if 𝔪 is
decomposable, then for any finitely generated R-module M of infinite projective dimension 𝔪 …

CLASSIFYING PROJECTIVE MODULES OVER SOME SEMILOCAL RINGS Page 1 September
12, 2007 10:10 WSPC/171-JAA 00252 Journal of Algebra and Its Applications Vol. 6, No. 5 …

Colocalizing subcategories of DRfi Page 1 J. reine angew. Math. 653 (2011), 221—243 DOI
10.1515/CRELLE.2011.028 Journal fr die reine und angewandte Mathematik ( Walter de …

Let R be a commutative Noetherian ring. Denote by mod R the category of finitely generated
R-modules. In this paper, we study dominant resolving subcategories of mod R. We …

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 …

This is the second part of our three-part study titled “A few examples of local rings.” In the first
part, we collected the basic tools and well-known important examples. But, since almost all …

We propose a definition of when a triangulated category should be considered a complete
intersection. We show (using work of Avramov and Gulliksen) that for the derived category of …

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 …