First, Second, and Third Change of Rings Theorems for Gorenstein Homological dimensions

Abstract

In this article, we investigate the change of rings theorems for the Gorenstein dimensions over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we extend the well-known first, second, and third change of rings theorems for the classical projective and injective dimensions to the Gorenstein projective and injective dimensions, respectively. Each of the results established in this article for the Gorenstein projective dimension is a generalization of a G-dimension of a finitely generated module M over a noetherian ring R.

Key Words:

• Change of rings results
• Classical homological dimensions
• Gorenstein homological dimensions
• Strongly Gorenstein projective and injective modules

2000 Mathematics Subject Classification:

• 13D02
• 13D05
• 13D07

ACKNOWLEDGMENT

The authors thank the referee for his/her careful reading of this work.

Notes

In this article, we refer to Weibel's book [19] for the projective case and to Kaplansky's book [15] for the injective case.

Communicated by I. Swanson.