Abstract:Abstract. Let (R, m, k) be a commutative Noetherian local ring. We study the suitable chains of semidualizing R-modules. We prove that when R is Artinian, the existence of a suitable chain of semidualizing modules of length n = max { i 0 | m i = 0 } implies that the the Poincaré series of k and the Bass series of R have very specific forms. Also, in this case we show that the Bass numbers of R are strictly increasing. This gives an insight into the question of Huneke about the Bass numbers of R.
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.