Constructing indecomposable integrally closed modules over a two-dimensional regular local ring

Futoshi Hayasaka

doi:10.1016/j.jalgebra.2020.03.029

Constructing indecomposable integrally closed modules over a two-dimensional regular local ring

Futoshi Hayasaka

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then we investigate their indecomposability. As a consequence, we have a large class of indecomposable integrally closed modules whose Fitting ideal is not simple. This gives an answer to Kodiyalam's question.

Original language	English
Pages (from-to)	879-907
Number of pages	29
Journal	Journal of Algebra
Volume	556
DOIs	https://doi.org/10.1016/j.jalgebra.2020.03.029
Publication status	Published - Aug 15 2020

Keywords

Indecomposable module
Integral closure
Monomial ideal
Regular local ring

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2020.03.029

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title = "Constructing indecomposable integrally closed modules over a two-dimensional regular local ring",

abstract = "In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then we investigate their indecomposability. As a consequence, we have a large class of indecomposable integrally closed modules whose Fitting ideal is not simple. This gives an answer to Kodiyalam's question.",

keywords = "Indecomposable module, Integral closure, Monomial ideal, Regular local ring",

author = "Futoshi Hayasaka",

note = "Funding Information: The author would like to thank Professors Shiro Goto, Yukio Nakamura and all the members of the seminar at Meiji University for their encouragement and many helpful suggestions at the early stage of this research. He would also like to thank Professor Ngo Viet Trung for informing him some papers on the decomposition of complete monomial ideals. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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AU - Hayasaka, Futoshi

N1 - Funding Information: The author would like to thank Professors Shiro Goto, Yukio Nakamura and all the members of the seminar at Meiji University for their encouragement and many helpful suggestions at the early stage of this research. He would also like to thank Professor Ngo Viet Trung for informing him some papers on the decomposition of complete monomial ideals. Publisher Copyright: © 2020 Elsevier Inc.

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Y1 - 2020/8/15

N2 - In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then we investigate their indecomposability. As a consequence, we have a large class of indecomposable integrally closed modules whose Fitting ideal is not simple. This gives an answer to Kodiyalam's question.

AB - In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then we investigate their indecomposability. As a consequence, we have a large class of indecomposable integrally closed modules whose Fitting ideal is not simple. This gives an answer to Kodiyalam's question.

KW - Indecomposable module

KW - Integral closure

KW - Monomial ideal

KW - Regular local ring

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Constructing indecomposable integrally closed modules over a two-dimensional regular local ring

Abstract

Keywords

ASJC Scopus subject areas

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