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• W2950202489 abstract "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 $Klotimes_R Klotimes_R L$ 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." @default.
• W2950202489 created "2019-06-27" @default.
• W2950202489 creator A5000224975 @default.
• W2950202489 creator A5014683161 @default.
• W2950202489 date "2004-04-20" @default.
• W2950202489 modified "2023-09-23" @default.
• W2950202489 title "The set of semidualizing complexes is a nontrivial metric space" @default.
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• W2950202489 hasPublicationYear "2004" @default.
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