Bass numbers and semidualizing complexes
Sean Sather-Wagstaff · 2009
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 2 n 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 2 n .We also show that, given a local ring homomorphism ϕ : R → S of finite flat dimension, if R and S admit dualizing complexes and if ϕ is not Gorenstein, then the cardinality of S(S) is at least twice the cardinality of S(R).