广义Gorenstein-Arf环

Pub Date : 2018-04-14 DOI:10.4310/ARKIV.2019.V57.N1.A3

Ela Celikbas, Olgur Celikbas, S. Goto, Naoki Taniguchi

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引用次数: 8

摘要

本文研究了广义Gorenstein-Arf环；一类严格包含在Gorenstein环类中的一维Cohen—Macaulay局部Arf环。我们得到了Arf环的新刻画和例子，并给出了我们的论点在数值半群环和某些理想化中的应用。特别地，我们推广了Barucci和Fr“oberg关于Arf数值半群环的一个漂亮结果。

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Generalized Gorenstein Arf rings

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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