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January, 2018 On the sequential polynomial type of modules
Shiro GOTO, Le Thanh NHAN
J. Math. Soc. Japan 70(1): 365-385 (January, 2018). DOI: 10.2969/jmsj/07017535


Let $M$ be a finitely generated module over a Noetherian local ring $R$. The sequential polynomial type $\mathrm{sp}(M)$ of $M$ was recently introduced by Nhan, Dung and Chau, which measures how far the module $M$ is from the class of sequentially Cohen–Macaulay modules. The present paper purposes to give a parametric characterization for $M$ to have $\mathrm{sp}(M)\le s$, where $s\ge -1$ is an integer. We also study the sequential polynomial type of certain specific rings and modules. As an application, we give an inequality between $\mathrm{sp}(S)$ and $\mathrm{sp}(S^G) $, where $S$ is a Noetherian local ring and $G$ is a finite subgroup of $\mathrm{Aut}S$ such that the order of $G$ is invertible in $S$.


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Shiro GOTO. Le Thanh NHAN. "On the sequential polynomial type of modules." J. Math. Soc. Japan 70 (1) 365 - 385, January, 2018.


Published: January, 2018
First available in Project Euclid: 26 January 2018

zbMATH: 06859856
MathSciNet: MR3750280
Digital Object Identifier: 10.2969/jmsj/07017535

Primary: 13C14 , 13D45 , 13E05

Keywords: distinguished system of parameters , sequentially Cohen–Macaulay module , strict $M$-sequence in dimension $>s$

Rights: Copyright © 2018 Mathematical Society of Japan


Vol.70 • No. 1 • January, 2018
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