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arXiv · 1611.05790

Chains of semidualizing modules

Ensiyeh Amanzadeh
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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 $n=\mathrm{max}\,\{\,i\geqslant 0\ |\ \mathfrak{m}^{i}\neq 0\,\}$ 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 $R$.

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Ensiyeh Amanzadeh. 2016-11-17. Chains of semidualizing modules. https://arxiv.org/abs/1611.05790

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