ZPI Property In Amalgamated Duplication Ring

Ahmed Hamed; Achraf Malek

doi:10.5666/KMJ.2022.62.2.205

Article

Kyungpook Mathematical Journal 2022; 62(2): 205-211

Published online June 30, 2022

ZPI Property In Amalgamated Duplication Ring

Ahmed Hamed and Achraf Malek^*

Department of Mathematics, Faculty of Sciences, Monastir, Tunisia
e-mail : hamed.ahmed@hotmail.fr and achraf_malek@yahoo.fr

Received: January 23, 2021; Revised: September 14, 2021; Accepted: December 6, 2021

Abstract

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Abstract

Let A be a commutative ring. We say that A is a ZPI ring if every proper ideal of A is a finite product of prime ideals [5]. In this paper, we study when the amalgamated duplication of A along an ideal I, A⋈ I to be a ZPI ring. We show that if I is an idempotent ideal of A, then A is a ZPI ring if and only if A⋈ I is a ZPI ring.

Keywords: ZPI ring, Amalgamated duplication ring, Dedekind domain