Generalized Gorenstein Arf rings
Ela Celikbas, Olgur Celikbas, Shiro Goto, and Naoki Taniguchi
TL;DR
This paper explores generalized Gorenstein Arf rings, providing new characterizations, examples, and applications to numerical semigroup rings, expanding understanding of this specific class within Cohen-Macaulay local rings.
Contribution
It introduces new characterizations and examples of generalized Gorenstein Arf rings and extends a key result to numerical semigroup rings.
Findings
New characterizations of generalized Gorenstein Arf rings
Examples illustrating the properties of these rings
Application to numerical semigroup rings and idealizations
Abstract
In this paper we study generalized Gorenstein Arf rings; a class of one-dimensional Cohen-Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We obtain new characterizations and examples of Arf rings, and give applications of our argument to numerical semigroup rings and certain idealizations. In particular, we generalize a beautiful result of Barucci and Fr\"oberg concerning Arf numerical semigroup rings.
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