Archiv der Mathematik· 2026Q2
Arf rings, simple singularities, and reflexive modules
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- Q2SCImago
- 2026year
Short summary
This paper extends the self-dual property of reflexive modules from Arf rings to higher-dimensional commutative Noetherian local rings.
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Key points
- Arf rings are characterized by the property that every reflexive module is isomorphic to its own dual.
- This self-duality property was previously shown to hold for Arf rings (one-dimensional).
- This paper explores whether this self-duality property extends to commutative Noetherian local rings of higher Krull dimension.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In a pandemic era preprint, Dao 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.
The authors' abstract, as published at the source. Archiv der Mathematik, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics