Journal of the Mathematical Society of Japan

On the sequential polynomial type of modules

Shiro GOTO and Le Thanh NHAN

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Abstract

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 $S$.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 1 (2018), 365-385.

Dates
First available in Project Euclid: 26 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1516957231

Digital Object Identifier
doi:10.2969/jmsj/07017535

Mathematical Reviews number (MathSciNet)
MR3750280

Zentralblatt MATH identifier
06859856

Subjects
Primary: 13E05: Noetherian rings and modules 13C14: Cohen-Macaulay modules [See also 13H10] 13D45: Local cohomology [See also 14B15]

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

Citation

GOTO, Shiro; NHAN, Le Thanh. On the sequential polynomial type of modules. J. Math. Soc. Japan 70 (2018), no. 1, 365--385. doi:10.2969/jmsj/07017535. https://projecteuclid.org/euclid.jmsj/1516957231


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