A locally F-finite Noetherian domain that is not F-finite

Tiberiu Dumitrescu; Cristodor Ionescu

doi:10.1216/jca.2022.14.177

Abstract

Using an old example of Nagata, we construct a Noetherian ring of prime characteristic $p$ , whose Frobenius morphism is locally finite, but not finite.

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Tiberiu Dumitrescu. Cristodor Ionescu. "A locally F-finite Noetherian domain that is not F-finite." J. Commut. Algebra 14 (2) 177 - 180, Summer 2022. https://doi.org/10.1216/jca.2022.14.177

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Received: 3 July 2020; Revised: 3 August 2020; Accepted: 4 August 2020; Published: Summer 2022

First available in Project Euclid: 14 July 2022

MathSciNet: MR4452656

zbMATH: 1497.13018

Digital Object Identifier: 10.1216/jca.2022.14.177

Subjects:

Primary: 13A35

Secondary: 13F40

Keywords: excellent rings , F-finite rings , Frobenius morphism

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