Chains of semidualizing modules

Abstract

Let $(R,\mathfrak{m},k)$ 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 $n=\max \{i⩾0|{\mathfrak{m}}^i\ne 0\}$ implies that the the Poincar$\acute{\mathrm{e}}$ 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 $R$.

9 pages

References in corpus (1)

• Growth in the minimal injective resolution of a local ring