Generalized gorenstein arf rings

Ela Celikbas, Olgur Celikbas, Shiro Goto, Naoki Endo

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)35-53
Number of pages19
JournalArkiv for Matematik
Volume57
Issue number1
DOIs
Publication statusPublished - 2019 Jan 1

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Numerical Semigroup
Semigroup Ring
Gorenstein Ring
Cohen-Macaulay Ring
Local Ring
Strictly
Ring
Generalise
Class

Keywords

  • Almost Gorenstein local rings
  • Arf rings
  • Generalized Gorenstein local rings

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Generalized gorenstein arf rings. / Celikbas, Ela; Celikbas, Olgur; Goto, Shiro; Endo, Naoki.

In: Arkiv for Matematik, Vol. 57, No. 1, 01.01.2019, p. 35-53.

Research output: Contribution to journalArticle

Celikbas, E, Celikbas, O, Goto, S & Endo, N 2019, 'Generalized gorenstein arf rings', Arkiv for Matematik, vol. 57, no. 1, pp. 35-53. https://doi.org/10.4310/ARKIV.2019.v57.n1.a3
Celikbas, Ela ; Celikbas, Olgur ; Goto, Shiro ; Endo, Naoki. / Generalized gorenstein arf rings. In: Arkiv for Matematik. 2019 ; Vol. 57, No. 1. pp. 35-53.
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