Complete intersection dimensions and Foxby classes
| dc.creator | Sather-Wagstaff, Sean | |
| dc.date | 2007-09-15 | |
| dc.date | 2008-05-27 | |
| dc.date.accessioned | 2026-07-07T09:40:44Z | |
| dc.date.available | 2026-07-07T09:40:44Z | |
| dc.description | Let $R$ be a local ring and $M$ a finitely generated $R$-module. The complete intersection dimension of $M$--defined by Avramov, Gasharov and Peeva, and denoted $\cidim_R(M)$--is a homological invariant whose finiteness implies that $M$ is similar to a module over a complete intersection. It is related to the classical projective dimension and to Auslander and Bridger's Gorenstein dimension by the inequalities $\gdim_R(N)\leq\cidim_R(N)\leq\pd_R(N)$. Using Blanco and Majadas' version of complete intersection dimension for local ring homomorphisms, we prove the following generalization of a theorem of Avramov and Foxby: Given local ring homomorphisms $ϕ\colon R\to S$ and $ψ\colon S\to T$ such that $ϕ$ has finite Gorenstein dimension, if $ψ$ has finite complete intersection dimension, then the composition $ψ\circϕ$ has finite Gorenstein dimension. This follows from our result stating that, if $M$ has finite complete intersection dimension, then $M$ is $C$-reflexive and is in the Auslander class $\catac(R)$ for each semidualizing $R$-complex $C$. | |
| dc.description | minor revisions, final version to appear in JPAA, 24 pages, uses xypic, Dedicated to Luchezar L. Avramov on the occasion of his sixtieth birthday | |
| dc.identifier | https://arxiv.org/abs/0709.2442 | |
| dc.identifier | http://arxiv.org/abs/0709.2442 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161580 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 13A35, 13B10, 13C05, 13D05, 13D07, 13D25, 14B25 | |
| dc.title | Complete intersection dimensions and Foxby classes | |
| dc.type | text |