Korean Journal of Mathematics

  • 제25권2호
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  • Pages.215-227
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  • 2017
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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GRADED INTEGRAL DOMAINS AND NAGATA RINGS, II

  • Chang, Gyu Whan (Department of Mathematics Education Incheon National University)
  • 투고 : 2017.03.07
  • 심사 : 2017.06.01
  • 발행 : 2017.06.30
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⟨ 이전 논문 다음 논문 ⟩

초록

Let D be an integral domain with quotient field K, X be an indeterminate over D, K[X] be the polynomial ring over K, and $R=\{f{\in}K[X]{\mid}f(0){\in}D\}$; so R is a subring of K[X] containing D[X]. For $f=a_0+a_1X+{\cdots}+a_nX^n{\in}R$, let C(f) be the ideal of R generated by $a_0$, $a_1X$, ${\ldots}$, $a_nX^n$ and $N(H)=\{g{\in}R{\mid}C(g)_{\upsilon}=R\}$. In this paper, we study two rings $R_{N(H)}$ and $Kr(R,{\upsilon})=\{{\frac{f}{g}}{\mid}f,g{\in}R,\;g{\neq}0,{\text{ and }}C(f){\subseteq}C(g)_{\upsilon}\}$. We then use these two rings to give some examples which show that the results of [4] are the best generalizations of Nagata rings and Kronecker function rings to graded integral domains.

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참고문헌

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피인용 문헌

  1. GRADED INTEGRAL DOMAINS AND PRÜFER-LIKE DOMAINS vol.54, pp.6, 2017, https://doi.org/10.4134/jkms.j160625
  2. Graded Prüfer domains vol.46, pp.2, 2018, https://doi.org/10.1080/00927872.2017.1327595
  3. Graded integral domains which are UMT-domains vol.46, pp.6, 2018, https://doi.org/10.1080/00927872.2017.1399406
  4. Graded integral domains in which each nonzero homogeneous $ t$ -ideal is divisorial vol.18, pp.1, 2017, https://doi.org/10.1142/s021949881950018x