2008/01/30 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean
Mathematics · #13D05 #13D25 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D05 #msc:13D25
paper · pdf · doi:10.48550/arxiv.0801.4743
v2: title changed, section 4 added, minor changes throughout; 10 pages
arxiv created 2009/03/13 · arxiv updated 2009/12/01
We investigate the set S(R) of shift-isomorphism classes of semidualizing R-complexes, ordered via the reflexivity relation, where R is a commutative noetherian local ring. Specifically, we study the question of whether S(R has cardinality 2n for some n. We show that, if there is a chain of length n in S(R) and if the reflexivity ordering on S(R) is transitive, then S(R) has cardinality at least 2n, and we explicitly describe some of its order-structure. We also show that, given a local ring homomorphism f: R→ S of finite flat dimension, if R and S admit dualizing complexes and if f is not Gorenstein, then the cardinality of S(S) is at least twice the cardinality of S(R).