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On ∗w-Finiteness Conditions

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경북대학교 자연과학대학 수학과|2023.12|Kyungpook Mathematical Journal|제63권 제4호|pp. 571-575|DOI https://doi.org/10.5666/KMJ.2023.63.4.571

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키워드

∗w-Noetherian domain∗w-principal ideal domain∗w-countable type ideal
주제분류수학

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).

Abstract

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).

참고문헌 (10)

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  2. S. El Baghdadi, "Semistar GCD domains", Comm. Algebra, 38, pp.3029~3044 (2010)
  3. R. Gilmer, "Multiplicative Ideal Theory", Queen's Papers in Pure Appl. Math, 90 (1992), Queen's University
  4. R. Gilmer, "Commutative Semigroup Rings" (1984), The Univ. of Chicago Press
  5. C. J. Hwang, "A note on w-Noetherian domains", Proc. Amer. Math. Soc, 141, pp.1199~1209 (2013)
  6. B. G. Kang, "On the converse of a well-known fact about Krull domains", J. Algebra, 124, pp.284~299 (1989)
  7. construction from Prufer domains and GCD-domains, "C. R. Math. Acad. Sci. Paris", 2011, 1135~1138
  8. J. W. Lim, "Chain conditions in special pullbacks", C. R. Math. Acad. Sci. Paris, 350, pp.655~659 (2012)
  9. F. Wang, "Foundations of Commutative Rings and Their Modules", Algebra and Applications, 22 (2016), Springer
  10. M. Zafrullah, "Ascending chain conditions and star operations", Comm. Algebra, 17, pp.1523~1533 (1989)

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