Korean Journal of Mathematics

  • 제20권2호
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  • Pages.185-191
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  • 2012
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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INTEGRAL DOMAINS WITH FINITELY MANY STAR OPERATIONS OF FINITE TYPE

  • 투고 : 2012.04.07
  • 심사 : 2012.06.10
  • 발행 : 2012.06.30
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⟨ 이전 논문 다음 논문 ⟩

초록

Let D be an integral domain and SF(D) be the set of star operations of finite type on D. We show that if ${\mid}SF(D){\mid}$ < ${\infty}$, then every maximal ideal of D is a $t$-ideal. We give an example of integrally closed quasi-local domains D in which the maximal ideal is divisorial (so a $t$-ideal) but ${\mid}SF(D){\mid}={\infty}$. We also study the integrally closed domains D with ${\mid}SF(D){\mid}{\leq}2$.

키워드

참고문헌

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피인용 문헌

  1. Some classification of certain integral domains via conductor overrings and semistar operations vol.49, pp.1, 2012, https://doi.org/10.1080/00927872.2020.1801708
  2. Finitely star regular domains vol.226, pp.7, 2022, https://doi.org/10.1016/j.jpaa.2021.106983