Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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ZPI Property In Amalgamated Duplication Ring

  • Hamed, Ahmed (Department of Mathematics, Faculty of Sciences) ;
  • Malek, Achraf (Department of Mathematics, Faculty of Sciences)
  • Received : 2021.01.23
  • Accepted : 2021.12.06
  • Published : 2022.06.30
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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.

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Acknowledgement

The authors would like to thank the referee for his/her insightful suggestions towards the improvement of the paper.

References

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