We study Auslander correspondence from the viewpoint of higher-dimensional analogue of
Auslander–Reiten theory [O. Iyama, Higher dimensional Auslander–Reiten theory on …

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 …

We establish a correspondence between recollements of abelian categories up to
equivalence and certain TTF-triples. For a module category we show, moreover, a …

Let R be a noetherian normal domain. We investigate when R admits a faithful module
whose endomorphism ring has finite global dimension. This can be viewed as a …

The representation dimension is an invariant introduced by Auslander to measure how far a
representation infinite algebra is from being representation finite. In 2005, Rouquier gave …

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a
noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also …

Wide subcategories of 𝑑-cluster tilting subcategories Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 373, Number 4, April 2020, Pages 2281–2309 …

Let Λ be an artin algebra and X a finitely generated Λ-module. Iyama has shown that there
exists a module Y such that the endomorphism ring Γ of X⊕ Y is quasi-hereditary, with a …

There are well-known constructions relating ring epimorphisms and tilting modules. The new
notion of silting module provides a wider framework for studying this interplay. To every …

Endomorphism Rings of Finite Global Dimension Page 1 Canad. J. Math. Vol. 59 (2), 2007 pp.
332–342 Endomorphism Rings of Finite Global Dimension Graham J. Leuschke Abstract. For …