Abstract
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).
Acknowledgments
The authors are grateful to the anonymous referee for careful reading and useful comments.
Citation
Ryotaro Isobe. Shinya Kumashiro. "Reflexive Modules over Arf Local Rings." Taiwanese J. Math. Advance Publication 1 - 11, 2024. https://doi.org/10.11650/tjm/240605
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