Abstract
In this paper we prove that for any associative ring R, and for any left R-module M with nite projective dimension, the Gorenstein injective dimension GidRM equals the usual injective dimension idRM. In particular, if GidRR is nite, then also idRR is nite, and thus R is Gorenstein (provided that R is commutative and Noetherian).
| Original language | English |
|---|---|
| Journal | Proceedings of the American Mathematical Society |
| Volume | 132 |
| Issue number | 5 |
| Pages (from-to) | 1279-1283 |
| ISSN | 0002-9939 |
| Publication status | Published - 2004 |