Arkiv för Matematik

Volume 57 (2019)

Number 1

Generalized Gorenstein Arf rings

Pages: 35 – 53

DOI: https://dx.doi.org/10.4310/ARKIV.2019.v57.n1.a3

Authors

Ela Celikbas (Department of Mathematics, West Virginia University, Morgantown, W.V., U.S.A.)

Olgur Celikbas (Department of Mathematics, West Virginia University, Morgantown, W.V., U.S.A.)

Shiro Goto (Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki, Japan)

Naoki Taniguchi (Global Education Center, Waseda University, Tokyo, Japan)

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.

Keywords

Arf rings, generalized Gorenstein local rings, almost Gorenstein local rings

2010 Mathematics Subject Classification

13A15, 13H10, 13H15

Full Text (PDF format)

Received 24 August 2018

Received revised 6 September 2018

Accepted 20 September 2018

Published 3 May 2019