2004/04/20 by Anders Frankild, Frankild, Anders, Sean Sather-Wagstaff +1
Mathematics · #05C12 #13B40 #13C05 #13C13 #13D05 #13D25 #13D40 #13H10 #54E35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #msc:05C12 #msc:13B40 #msc:13C05 #msc:13C13 #msc:13D05 #msc:13D25 #msc:13D40 #msc:13H10 #msc:54E35
paper · pdf · doi:10.48550/arxiv.math/0404361
Final version (to appear in J. Algebra) has been extensively reorganized
openalex publication_date 2004/04/20 · arxiv created 2006/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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\lotimesR K\lotimesR 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.