East Asian mathematical journal

  • 제34권5호
  • /
  • Pages.571-575
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  • 2018
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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THE COHEN TYPE THEOREM FOR S-⁎ω-PRINCIPAL IDEAL DOMAINS

  • Lim, Jung Wook (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • 투고 : 2018.01.29
  • 심사 : 2018.07.04
  • 발행 : 2018.09.30
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초록

Let D be an integral domain, ${\ast}$ a star-operation on D, and S a (not necessarily saturated) multiplicative subset of D. In this article, we prove the Cohen type theorem for $S-{\ast}_{\omega}$-principal ideal domains, which states that D is an $S-{\ast}_{\omega}$-principal ideal domain if and only if every nonzero prime ideal of D (disjoint from S) is $S-{\ast}_{\omega}$-principal.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

참고문헌

  1. D.D. Anderson and T. Dumitrescu, S-Noetherian rings, Comm. Algebra 30 (2002), 4407-4416. https://doi.org/10.1081/AGB-120013328
  2. 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
  3. I. Kaplansky, Commutative Rings, Polygonal Publishing House, Washington, New Jersey, 1994.
  4. H. Kim, M.O. Kim, and J.W. Lim, On S-strong Mori domains, J. Algebra 416 (2014), 314-332. https://doi.org/10.1016/j.jalgebra.2014.06.015
  5. H. Kim and J.W. Lim, On S-$*_w$-principal ideal domains, Algebra Colloq. 25 (2018), 217-224. https://doi.org/10.1142/S1005386718000159