The set of semidualizing complexes is a nontrivial metric space
| dc.creator | Frankild, Anders | |
| dc.creator | Sather-Wagstaff, Sean | |
| dc.date | 2004-04-20 | |
| dc.date | 2006-07-17 | |
| dc.date.accessioned | 2026-07-07T06:36:43Z | |
| dc.date.available | 2026-07-07T06:36:43Z | |
| dc.description | We show that the set $\s(R)$ of shift-isomorphism classes of semidualizing complexes over a local ring $R$ admits a nontrivial metric. We investigate the interplay between the metric and several algebraic operations. Motivated by the dagger duality isometry, we prove the following: If $K,L$ are homologically bounded below and degreewise finite $R$-complexes such that $K\lotimes_R K\lotimes_R L$ is semidualizing, then $K$ is shift-isomorphic to $R$. In investigating the existence of nontrivial open balls in $\s(R)$, we prove that $\s(R)$ contains elements that are not comparable in the reflexivity ordering if and only if it contains at least three distinct elements. | |
| dc.description | Final version (to appear in J. Algebra) has been extensively reorganized | |
| dc.identifier | https://arxiv.org/abs/math/0404361 | |
| dc.identifier | http://arxiv.org/abs/math/0404361 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100174 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13B40, 13C05, 13C13, 13D05, 13D25, 13D40, 13H10, 05C12, 54E35 | |
| dc.title | The set of semidualizing complexes is a nontrivial metric space | |
| dc.type | text |