Kyungpook Mathematical Journal

  • 제63권4호
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  • Pages.571-575
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  • 2023
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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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On *w-Finiteness Conditions

  • Jung Wook Lim (Department of Mathematics, Kyungpook National University)
  • 투고 : 2023.07.14
  • 심사 : 2023.07.31
  • 발행 : 2023.12.31
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초록

Let D be an integral domain and let * be a star-operation on D. In this article, we give new characterizations of *w-Noetherian domains and *w-principal ideal domains. More precisely, we show that D is a *w-Noetherian domain (resp., *w-principal ideal domain) if and only if every *w-countable type ideal of D is of *w-finite type (resp., principal).

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참고문헌

  1. D. D. Anderson and S. J. Cook, Two star-operations and their induced lattices, Comm. Algebra, 28(2000), 2461-2475. https://doi.org/10.1080/00927870008826970
  2. S. El Baghdadi, Semistar GCD domains, Comm. Algebra, 38(2010), 3029-3044. https://doi.org/10.1080/00927870903114961
  3. R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure Appl. Math., vol. 90, Queen's University, Kingston, Ontario, Canada, 1992.
  4. R. Gilmer, Commutative Semigroup Rings, The Univ. of Chicago Press, Chicago and London, 1984.
  5. C. J. Hwang and J. W. Lim, A note on *w-Noetherian domains, Proc. Amer. Math. Soc., 141(2013), 1199-1209. https://doi.org/10.1090/S0002-9939-2012-10706-3
  6. B. G. Kang, On the converse of a well-known fact about Krull domains, J. Algebra, 124(1989), 284-299. https://doi.org/10.1016/0021-8693(89)90131-2
  7. J. W. Lim, The D + E[Γ*] construction from Prüfer domains and GCD-domains, C. R. Math. Acad. Sci. Paris, 349(2011), 1135-1138. https://doi.org/10.1016/j.crma.2011.10.023
  8. J. W. Lim and D. Y. Oh, Chain conditions in special pullbacks, C. R. Math. Acad. Sci. Paris, 350(2012), 655-659. https://doi.org/10.1016/j.crma.2012.07.003
  9. F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Algebra and Applications, vol. 22, Springer, Singapore, 2016.
  10. M. Zafrullah, Ascending chain conditions and star operations, Comm. Algebra, 17(1989), 1523-1533. https://doi.org/10.1080/00927878908823804