Kyungpook Mathematical Journal 2022; 62(2): 205-211
Published online June 30, 2022
Copyright © Kyungpook Mathematical Journal.
ZPI Property In Amalgamated Duplication Ring
Ahmed Hamed and Achraf Malek*
Department of Mathematics, Faculty of Sciences, Monastir, Tunisia
e-mail : email@example.com and firstname.lastname@example.org
Received: January 23, 2021; Revised: September 14, 2021; Accepted: December 6, 2021
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 . 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