The purpose of this work is to study commutative Noetherian rings by studying certain
subcategories of the category of finitely generated modules over such rings. We begin by …

A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich
modules split. In this paper we initiate the study of Ulrich split rings. We prove several …

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 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 …

Let $ R $ be a commutative noetherian local ring and denote by $\operatorname {mod} R $
the category of finitely generated $ R $-modules. In this paper, we give some evaluations of …

In this paper we extend two results of Happel to commutative rings. Let $(A,\mathfrak {m}) $
be a commutative Noetherian local ring. Let $ D^ b_f (mod\A) $ be the bounded derived …

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 commutative noetherian local ring. As an analog of the notion of the dimension of
a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of …

Let C be a subcategory of the category of finitely generated R-modules over a commutative
noetheian ring R. We prove that, if C is closed under images and extensions (which we call …

Let R be a commutative noetherian ring. Denote by mod\, R mod R the category of finitely
generated R-modules. In this paper, we study n-torsionfree modules in the sense of …