The radical of an $n$-absorbing ideal

Hyun Seung Choi; Andrew Walker

doi:10.1216/jca.2020.12.171

Abstract

In this note, we show that in a commutative ring $R$ with unity, for any $n > 0$ , if $I$ is an $n$ -absorbing ideal of $R$ , then ${(\sqrt{I})}^{n} \subseteq I$ .

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Hyun Seung Choi. Andrew Walker. "The radical of an $n$-absorbing ideal." J. Commut. Algebra 12 (2) 171 - 177, Summer 2020. https://doi.org/10.1216/jca.2020.12.171

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Received: 3 March 2017; Revised: 18 August 2017; Accepted: 24 August 2017; Published: Summer 2020

First available in Project Euclid: 2 June 2020

zbMATH: 07211333

MathSciNet: MR4105542

Digital Object Identifier: 10.1216/jca.2020.12.171

Subjects:

Primary: 13A15

Keywords: $2$-absorbing ideal , $n$-absorbing ideal , effective Nullstellensatz , strongly $n$-absorbing ideal

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