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 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 …

In this paper we study homological dimensions of finitely generated modules over
commutative Noetherian local rings, called reducing homological dimensions. We obtain …

We classify certain resolving subcategories of finitely generated modules over a
commutative noetherian ring R by using integer-valued functions on SpecR. As an …

We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can
be used as test modules, which detect finite homological dimensions of modules. We prove …

EXACT SUBCATEGORIES, SUBFUNCTORS OF EXT, AND SOME APPLICATIONS Page 1
Nagoya Math. J., (2023), 1–41 DOI 10.1017/nmj.2023.29 EXACT SUBCATEGORIES …

Let R be a Cohen–Macaulay local ring. In this paper, we study the structure of Ulrich R-
modules mainly in the case where R has minimal multiplicity. We explore generation of …

In this article we present a systematic study of the reflexivity properties of homologically finite
complexes with respect to semidualizing complexes in the setting of nonlocal rings. One …

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 …

We develop the theory of trace modules up to isomorphism and explore the relationship
between preenveloping classes of modules and the property of being a trace module …