The set of semidualizing complexes is a nontrivial metric space

dc.creatorFrankild, Anders
dc.creatorSather-Wagstaff, Sean
dc.date2004-04-20
dc.date2006-07-17
dc.date.accessioned2026-07-07T06:36:43Z
dc.date.available2026-07-07T06:36:43Z
dc.descriptionWe 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.descriptionFinal version (to appear in J. Algebra) has been extensively reorganized
dc.identifierhttps://arxiv.org/abs/math/0404361
dc.identifierhttp://arxiv.org/abs/math/0404361
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100174
dc.subjectCommutative Algebra
dc.subject13B40, 13C05, 13C13, 13D05, 13D25, 13D40, 13H10, 05C12, 54E35
dc.titleThe set of semidualizing complexes is a nontrivial metric space
dc.typetext

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