ON THE UBIQUITY OF ARF RINGS

Ela Celikbas; Olgur Celikbas; Cătălin Ciupercă; Naoki Endo; Shiro Goto; Ryotaro Isobe; Naoyuki Matsuoka

doi:10.1216/jca.2023.15.177

Abstract

We introduce and develop the theory of weakly Arf rings, generalizing the Arf rings originally defined by J. Lipman in 1971. We provide characterizations of the weakly Arf rings and study their relation with the Arf rings and the strictly closed rings. Furthermore, we give various examples of weakly Arf rings that come from idealizations, fiber products, determinantal rings, and invariant subrings.

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Ela Celikbas. Olgur Celikbas. Cătălin Ciupercă. Naoki Endo. Shiro Goto. Ryotaro Isobe. Naoyuki Matsuoka. "ON THE UBIQUITY OF ARF RINGS." J. Commut. Algebra 15 (2) 177 - 231, Summer 2023. https://doi.org/10.1216/jca.2023.15.177

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Received: 31 May 2021; Revised: 29 November 2021; Accepted: 14 December 2021; Published: Summer 2023

First available in Project Euclid: 29 June 2023

MathSciNet: MR4611108

zbMATH: 07725183

Digital Object Identifier: 10.1216/jca.2023.15.177

Subjects:

Primary: 13A15 , 13B22 , 13B30

Keywords: Arf ring , strictly closed ring , weakly Arf ring

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