Generalized Gorenstein Arf rings

Ela Celikbas West Virginia University Olgur Celikbas West Virginia University Shiro Goto Meiji University Naoki Taniguchi Waseda University

Arithmetic Geometry and Commutative Algebra mathscidoc:1912.43028

Arkiv for Matematik, 57, (1), 35-53, 2019
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.
Arf rings, generalized Gorenstein local rings, almost Gorenstein local rings
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@inproceedings{ela2019generalized,
  title={Generalized Gorenstein Arf rings},
  author={Ela Celikbas, Olgur Celikbas, Shiro Goto, and Naoki Taniguchi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204132818106245584},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={1},
  pages={35-53},
  year={2019},
}
Ela Celikbas, Olgur Celikbas, Shiro Goto, and Naoki Taniguchi. Generalized Gorenstein Arf rings. 2019. Vol. 57. In Arkiv for Matematik. pp.35-53. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204132818106245584.
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