Syzygy modules for quasi $k$-Gorenstein rings
| dc.creator | Huang, Zhaoyong | |
| dc.date | 2004-09-10 | |
| dc.date.accessioned | 2026-07-07T05:12:01Z | |
| dc.date.available | 2026-07-07T05:12:01Z | |
| dc.description | Let $Λ$ be a quasi $k$-Gorenstein ring. For each $d$th syzygy module $M$ in mod $Λ$ (where $0 \leq d \leq k-1$), we obtain an exact sequence $0 \to B \to M \bigoplus P \to C \to 0$ in mod $Λ$ with the properties that it is dual exact, $P$ is projective, $C$ is a $(d+1)$st syzygy module, $B$ is a $d$th syzygy of Ext$_Λ^{d+1}(D(M), Λ)$ and the right projective dimension of $B^*$ is less than or equal to $d-1$. We then give some applications of such an exact sequence as follows. (1) We obtain a chain of epimorphisms concerning $M$, and by dualizing it we then get the spherical filtration of Auslander and Bridger for $M^*$. (2) We get Auslander and Bridger's Approximation Theorem for each reflexive module in mod $Λ^{op}$. (3) We show that for any $0 \leq d \leq k-1$ each $d$th syzygy module in mod $Λ$ has an Evans-Griffith representation. As an immediate consequence of (3), we have that, if $Λ$ is a commutative noetherian ring with finite self-injective dimension, then for any non-negative integer $d$, each $d$th syzygy module in mod $Λ$ has an Evans-Griffith representation, which generalizes an Evans and Griffith's result to much more general setting. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409174 | |
| dc.identifier | http://arxiv.org/abs/math/0409174 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72437 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.subject | 16E30; 16E65; 16P40 | |
| dc.title | Syzygy modules for quasi $k$-Gorenstein rings | |
| dc.type | text |