Henrik Holm

TL;DR: In this paper, the closely related Gorenstein projective, Goren stein injective and 2-at dimensions of modules are studied, and a generalization of these results is given to give homological descriptions of the GORNE dimensions over arbitrary associative rings.

TL;DR: Gorenstein homological dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings as discussed by the authors, and the class of rings known to admit good criteria for Finiteness of Gorenstein dimensions: it now includes, for instance, the rings encountered in Commutative Algebraic geometry and, in the non-commutative realm, $k$--algebras with a dualizing complex.

TL;DR: Gorenstein homological dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings as mentioned in this paper, and the class of rings known to admit good criteria for Finiteness of Gorenstein dimensions:

TL;DR: A semi-dualizing module over a commutative noetherian ring is a finitely generated module C with RHom A (C, C ) ≈ A in the derived category D (A ) as discussed by the authors.

TL;DR: In this article, the authors extend the definition of a semidualizing module to general associative rings, which enables them to define and study Auslander and Bass classes with respect to a semi-dualizing bimodule.