Arf rings, simple singularities and reflexive modules

Özgür Esentepe

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arXiv · 2505.16568

Arf rings, simple singularities and reflexive modules

Özgür Esentepe

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Abstract

In a pandemic era preprint, Dao showed showed two remarkable properties of Arf rings: under some mild conditions, they admit finitely many indecomposable reflexive modules up to isomorphism and every reflexive module is actually isomorphic to its own dual. In fact, the latter property characterises Arf rings. Arf rings are one dimensional rings and it is natural to wonder what happens in higher Krull dimension. In this paper, we investigate the self-dual property for commutative Noetherian local rings.

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Özgür Esentepe. 2025-05-22. Arf rings, simple singularities and reflexive modules. https://arxiv.org/abs/2505.16568

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