Lower bounds for the number of semidualizing complexes over a local ring
| dc.creator | Sather-Wagstaff, Sean | |
| dc.date | 2008-01-30 | |
| dc.date | 2009-03-13 | |
| dc.date.accessioned | 2026-07-07T12:51:44Z | |
| dc.date.available | 2026-07-07T12:51:44Z | |
| dc.description | We investigate the set S(R) of shift-isomorphism classes of semidualizing R-complexes, ordered via the reflexivity relation, where R is a commutative noetherian local ring. Specifically, we study the question of whether S(R$ has cardinality 2^n for some n. We show that, if there is a chain of length n in S(R) and if the reflexivity ordering on S(R) is transitive, then S(R) has cardinality at least 2^n, and we explicitly describe some of its order-structure. We also show that, given a local ring homomorphism f: R\to S of finite flat dimension, if R and S admit dualizing complexes and if f is not Gorenstein, then the cardinality of S(S) is at least twice the cardinality of S(R). | |
| dc.description | v2: title changed, section 4 added, minor changes throughout; 10 pages | |
| dc.identifier | https://arxiv.org/abs/0801.4743 | |
| dc.identifier | http://arxiv.org/abs/0801.4743 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223086 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D05, 13D25 | |
| dc.title | Lower bounds for the number of semidualizing complexes over a local ring | |
| dc.type | text |