Generalized gorenstein arf rings

Ela Celikbas; Olgur Celikbas; Shiro Goto; Naoki Endo

doi:10.4310/ARKIV.2019.v57.n1.a3

Generalized gorenstein arf rings

Ela Celikbas, Olgur Celikbas, Shiro Goto, Naoki Endo

Global Education Center

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 Fröberg concerning Arf numerical semigroup rings.

Original language	English
Pages (from-to)	35-53
Number of pages	19
Journal	Arkiv for Matematik
Volume	57
Issue number	1
DOIs	https://doi.org/10.4310/ARKIV.2019.v57.n1.a3
Publication status	Published - 2019 Jan 1

Keywords

Almost Gorenstein local rings
Arf rings
Generalized Gorenstein local rings

ASJC Scopus subject areas

Mathematics(all)

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10.4310/ARKIV.2019.v57.n1.a3

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AU - Celikbas, Ela

AU - Celikbas, Olgur

AU - Goto, Shiro

AU - Endo, Naoki

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 Fröberg concerning Arf numerical semigroup rings.

AB - 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 Fröberg concerning Arf numerical semigroup rings.

KW - Almost Gorenstein local rings

KW - Arf rings

KW - Generalized Gorenstein local rings

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JF - Arkiv for Matematik

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Generalized gorenstein arf rings

Abstract

Keywords

ASJC Scopus subject areas

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