It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

For a finite‐dimensional algebra A, we establish correspondences between torsion classes
and wide subcategories in mod (A). In case A is representation finite, we obtain an explicit …

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 this paper, we study the relationship between wide subcategories and torsion classes of
an abelian length category AA from the point of view of lattice theory. Motivated by τ-tilting …

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 …

For an arbitrary finite dimensional algebra $\Lambda $, we prove that any wide subcategory
of $\mathsf {mod}\Lambda $ satisfying a certain finiteness condition is $\theta $-semistable …

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 …

In this paper, we study ICE-closed (= Image-Cokernel-Extension-closed) subcategories of
an abelian length category using torsion classes. To each interval [U, T] in the lattice of …

Let $\Lambda $ be a finite-dimensional algebra. A wide subcategory of $\mathsf
{mod}\Lambda $ is called left finite if the smallest torsion class containing it is functorially …

Let R be a commutative noetherian ring and I an ideal of R. Assume that for all integers i the
local cohomology module HI i (R) is I-cofinite. Suppose that R p is a regular local ring for all …