Various classification theorems of thick subcategories of a triangulated category have been
obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the …

In a recent paper, Iyama and Yoshino considered two interesting examples of isolated
singularities over which it is possible to classify the indecomposable maximal Cohen …

Let R be a (possibly noncommutative) ring and let C be a class of finitely generated (right) R-
modules which is closed under finite direct sums, direct summands, and isomorphisms …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …

Let be a commutative noetherian local ring of Krull dimension. We prove that the
cohomology annihilator of contains a power of if and only if, for some the th syzygies in are …

The notion of local rings with quasi-decomposable maximal ideal was formally introduced by
Nasseh and Takahashi. In separate works, the authors of the present paper showed that …

We extend the classification of finitely generated modules and the combinatorial description
of Auslander-Reiten sequences for finite-dimensional string algebras to infinite dimensional …

Abstract Let φ: R→ S be a flat local homomorphism between commutative Noetherian local
rings. In this paper, the ascent and descent of Artinian module structures between R and S …

We investigate the interplay between properties of Ext modules and the ascent of module
structures along local ring homomorphisms. Specifically, let $\varphi\colon (R,\mathfrak {m} …