English

Reflexive modules over Arf local rings

Commutative Algebra 2023-12-27 v2

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.

Keywords

Cite

@article{arxiv.2105.07184,
  title  = {Reflexive modules over Arf local rings},
  author = {Ryotaro Isobe and Shinya Kumashiro},
  journal= {arXiv preprint arXiv:2105.07184},
  year   = {2023}
}

Comments

9 pages

R2 v1 2026-06-24T02:08:19.505Z