Gorenstein homological dimensions and Auslander categories
| dc.creator | Esmkhani, Mohammad Ali | |
| dc.creator | Tousi, Massoud | |
| dc.date | 2005-11-24 | |
| dc.date | 2006-06-27 | |
| dc.date.accessioned | 2026-07-07T06:51:42Z | |
| dc.date.available | 2026-07-07T06:51:42Z | |
| dc.description | In this paper, we study Gorenstein injective, projective, and flat modules over a Noetherian ring $R$. For an $R$-module $M$, we denote by ${\rm Gpd}_RM$ and ${\rm Gfd}_R M$ the Gorenstein projective and flat dimensions of $M$, respectively. We show that ${\rm Gpd}_RM<\infty$ if and only if ${\rm Gfd}_RM<\infty$ provided the Krull dimension of $R$ is finite. Moreover, in the case that $R$ is local, we correspond to a dualizing complex ${\bf D}$ of $\hat{R}$, the classes $A'(R)$ and $B'(R)$ of $R$-modules. For a module $M$ over a local ring $R$, we show that $M\in A'(R)$ if and only if ${\rm Gpd}_RM<\infty$ or equivalently ${\rm Gfd}_RM<\infty$. In dual situation by using the class $B'(R)$, we provide a characterization of Gorenstein injective modules. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511612 | |
| dc.identifier | http://arxiv.org/abs/math/0511612 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105073 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Primary 13D05, 13D07; Secondary 13H10, 13C10 | |
| dc.title | Gorenstein homological dimensions and Auslander categories | |
| dc.type | text |