Open Access
2024 Reflexive Modules over Arf Local Rings
Ryotaro Isobe, Shinya Kumashiro
Author Affiliations +
Taiwanese J. Math. Advance Publication 1-11 (2024). DOI: 10.11650/tjm/240605


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.

Funding Statement

The first author was supported by JSPS KAKENHI Grant Number JP21K13767. The second author was supported by JSPS KAKENHI Grant Number JP21K13766 and by Grant for Basic Science Research Projects from the Sumitomo Foundation (Grant number 2200259).


The authors are grateful to the anonymous referee for careful reading and useful comments.


Download Citation

Ryotaro Isobe. Shinya Kumashiro. "Reflexive Modules over Arf Local Rings." Taiwanese J. Math. Advance Publication 1 - 11, 2024.


Published: 2024
First available in Project Euclid: 19 June 2024

Digital Object Identifier: 10.11650/tjm/240605

Primary: 13B22 , 13C05 , 13H10

Keywords: Arf ring , integrally closed ideal , reflexive module , trace ideal

Rights: Copyright © 2024 The Mathematical Society of the Republic of China

Advance Publication
Back to Top