A new characterization of discrete valuation rings

Reza Naghipour; Monireh Sedghi

doi:10.32513/asetmj/19322008231

Abstract

The aim of this paper is to give a new characterization of discrete valuation rings, namely, it is shown that if $(D, \frak m)$ is a local (Noetherian) ring such that depth $D>0$ and $\frak m^k$ is principal ideal for some integer $k\geq 1$ , then $D$ is a discrete valuation ring.

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The current pdf replaces the original pdf file, first available on 22 December 2022. The new version corrects the DOI prefix to read 10.32513.

Acknowledgments

The authors are deeply grateful to the referee for suggesting many improvements on the paper. Also, we would like to thank Professor Kamal Bahmanpour for his reading of the first draft and valuable discussions.

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Reza Naghipour. Monireh Sedghi. "A new characterization of discrete valuation rings." Adv. Studies: Euro-Tbilisi Math. J. 15 (4) 141 - 144, December 2022. https://doi.org/10.32513/asetmj/19322008231

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Received: 4 August 2022; Accepted: 20 October 2022; Published: December 2022

First available in Project Euclid: 22 December 2022

MathSciNet: MR4525447

zbMATH: 1504.13007

Digital Object Identifier: 10.32513/asetmj/19322008231

Subjects:

Primary: 13A18

Secondary: 13F10

Keywords: Discrete valuation ring , Gorenstein ring , socle

Abstract

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