Reflexive Modules over Arf Local Rings

被引：1

作者：

Isobe, Ryotaro ^{[1
]}

Kumashiro, Shinya ^{[2
]}

机构：

[1] Oshima Coll, Natl Inst Technol, Gen Educ Div, 1091-1 Oazakomatsu, Suooshima, Yamaguchi 7422193, Japan

[2] Osaka Inst Technol, Dept Math, 5-16-1 Omiya,Asahi Ku, Osaka 5358585, Japan

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2024年 / 28卷 / 05期

关键词：

reflexive module; Arf ring; integrally closed ideal; trace ideal; IDEALS;

D O I：

10.11650/tjm/240605

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a certain direct -sum decomposition of reflexive modules over (one-dimensional) Arf local rings. We also see the equivalence of three notions, say, integrally closed ideals, trace ideals, and reflexive modules of rank one (i.e., divisorial ideals) up to isomorphisms in Arf rings. As an application, we obtain the finiteness of indecomposable reflexive modules, up to isomorphism, for analytically irreducible Arf local rings.

引用

页码：865 / 875

页数：11

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