Kyungpook Mathematical Journal

  • 제62권2호
  • /
  • Pages.205-211
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  • 2022
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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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)
  • 투고 : 2021.01.23
  • 심사 : 2021.12.06
  • 발행 : 2022.06.30
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초록

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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과제정보

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

참고문헌

  1. M. D'Anna, C. A. Finocchiaro and M. Fantana, Properties of chains of prime ideal of amalgamated algebra along an ideal, J. Pure Appl. Algebra, 214(9)(2010), 1633-1641. https://doi.org/10.1016/j.jpaa.2009.12.008
  2. M. D'Anna, C. A. Finocchiaro and M. Fantana, Amalgamated algebra along an ideal, Commutative algebra and its applications, 155-172.
  3. M. D'Anna, A construction of Gorenstein rings, J. Algebra, 306(2)(2006), 507-519. https://doi.org/10.1016/j.jalgebra.2005.12.023
  4. M. D'Anna and M. Fontana, The amalgamated duplication of ring along an ideal: the basic properties, J. Algebra Appl., 6(2007), 241-252.
  5. H. S. Butts and R. Gilmer, Primary ideals and prime power ideals, Canadian J. Math., 18(1966), 1183-1195. https://doi.org/10.4153/CJM-1966-117-9
  6. A. Hamed and S. Hizem, S-Noetherian rings of the forms 𝒜[X] and 𝒜[[X]], Comm. Algebra, 43(9)(2015), 3848-3856. https://doi.org/10.1080/00927872.2014.924127
  7. M. Larsen, and P. McCarthy, Multiplicative theory of ideals, Pure and Applied Mathematics, Academic Press, New York(1971).
  8. K. B. Levitz, A Charecterization of General Z.P.I-Rings, Proc. Amer. Math. Soc., 32(2)(1972), 376-380. https://doi.org/10.1090/S0002-9939-1972-0294312-5
  9. C. A. Wood, On General Z.P.I-Rings, Pacific J. Math., 30(3)(1969), 837-846. https://doi.org/10.2140/pjm.1969.30.837