Mathematics – Commutative Algebra
Scientific paper
2005-11-24
Mathematics
Commutative Algebra
15 pages
Scientific paper
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.
Esmkhani Mohammad Ali
Tousi Massoud
No associations
LandOfFree
Gorenstein homological dimensions and Auslander categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Gorenstein homological dimensions and Auslander categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gorenstein homological dimensions and Auslander categories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-424667