On Gorenstein projective, injective and flat dimensions - A functorial description with applications

JOURNAL OF ALGEBRA

卷:302

Article

Christensen, Lars Winther ; Frankild, Anders ; Holm, Henrik

关键词: Gorenstein projective dimension;    Gorenstein injective dimension;    Gorenstein flat dimension;    Auslander categories;    Foxby equivalence;    bass formula;    Chouinard formula;    dualizing complex;   

DOI  :  10.1016/j.jalgebra.2005.12.007

来源: Elsevier

【 摘 要 】

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings. In this paper we enlarge the class of rings known to admit good criteria for finiteness of Gorenstein dimensions: e It now includes, for instance, the rings encountered in commutative algebraic geometry and, in the noncommutative realm, k-algebras with a dualizing complex. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free