Local rings of embedding codepth at most 3 have only trivial semidualizing complexes

2013/12/31 by Saeed Nasseh, Nasseh, Saeed, Sean Sather-Wagstaff +1
Mathematics · #13D09 #13E10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13D02 #Secondary: 13D05 #math.AC #msc:13D02 #msc:13D05 #msc:13D09 #msc:13E10

paper · pdf · doi:10.48550/arxiv.1401.0210

9 pages

arxiv created 2013/12/31 · arxiv updated 2014/01/03

Abstract

We prove that a local ring R of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, R itself and a dualizing R-complex if one exists.

Related

• Lower bounds for the number of semidualizing complexes over a local ring
• Characterizing certain semidualizing complexes via their Betti and Bass numbers
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• Presentations of rings with a chain of semidualizing modules