The Cohen type theorem and the Eakin–Nagata type theorem for $S$-Noetherian rings revisited

Dong Kyu Kim; Jung Wook Lim

doi:10.1216/rmj.2020.50.619

Abstract

We give a new proof of the Cohen type theorem for $S$ -Noetherian rings and a slight generalization of the Eakin–Nagata type theorem for $S$ -Noetherian rings.

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Dong Kyu Kim. Jung Wook Lim. "The Cohen type theorem and the Eakin–Nagata type theorem for $S$-Noetherian rings revisited." Rocky Mountain J. Math. 50 (2) 619 - 630, April 2020. https://doi.org/10.1216/rmj.2020.50.619

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Received: 9 July 2019; Revised: 6 September 2019; Accepted: 22 October 2019; Published: April 2020

First available in Project Euclid: 29 May 2020

zbMATH: 07210983

MathSciNet: MR4104398

Digital Object Identifier: 10.1216/rmj.2020.50.619

Subjects:

Primary: 13A15 , 13E99 , 16D25 , 16P99

Keywords: $S$-Noetherian module , (right) $S$-Noetherian ring , Cohen type theorem , Eakin–Nagata type theorem

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