The set of semidualizing complexes is a nontrivial metric space
By Anders J. Frankild, Sean Sather-Wagstaff. 2004
55 citations recorded by the source corpus.
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 K ⊗ R L K ⊗ R L 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/29108fac20190a9437a036b83b597f15eab2de08
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Comparison of relative cohomology theories with respect to semidualizing modules (2007, methodology): “For discussions of methods for generating other nonisomorphic semidualizing modules B and C such that GPC -p dR(B ) 18 ,25].”