Kyungpook Mathematical Journal

  • 제61권4호
  • /
  • Pages.823-830
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  • 2021
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Characterization of Prime and Maximal Ideals of Product Rings by 𝓕 - lim

  • Mouadi, Hassan (Faculty of Sciences and Technology Mohammedia, University Hassan 2 of Casablanca) ;
  • Karim, Driss (Faculty of Sciences and Technology Mohammedia, University Hassan 2 of Casablanca)
  • 투고 : 2021.02.02
  • 심사 : 2021.07.12
  • 발행 : 2021.12.31
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초록

Let {Ri}i∈I be an infinite family of rings and R = ∏i∈I Ri their product. In this paper, we investigate the prime spectrum of R by 𝓕-limits. Special attention is paid to relationship between the elements of Spec(Ri) and the elements of Spec(∏i∈I Ri) use 𝓕-lim, also we give a new condition so that ∏i∈I Ri is a zero dimensional ring.

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과제정보

We would like to thank the referee for his/her useful comments which help to improve the quality of this manuscript.

참고문헌

  1. M. F. Atiyah, I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Company, Reading, 1969.
  2. R. Gilmer, Zero-dimensional extension rings and subrings, Zero-dimensional Commutative Rings, Lecture Notes in Pure and Appl. Math., 171(1995), 27-39.
  3. R. Gilmer, W. Heinzer, Product of commutative rings and zero-dimensionality, Trans. Amer. Math. Soc., 331(2)(1992), 663-680. https://doi.org/10.2307/2154134
  4. S. Garcia-Ferreira, L. M. Ruza-Montilla, The 𝓕 - lim of a Sequence of Prime Ideals, Comm. Algebra, 39(7)(2011), 2532-2544. https://doi.org/10.1080/00927872.2010.491492
  5. J. Shapiro, The Prime Spectrum of an Infinite Product of Zero-Dimensional Rings, Zero-Dimensional Rings, Lecture Notes in Pure and Appl. Math., 171(1995), 375-481.