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ON GRADED KRULL OVERRINGS OF A GRADED NOETHERIAN DOMAIN

박미희|이은경
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회보 (Bulletin of the KMS)|제49권 제1호|pp. 205-211

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참고문헌

키워드

graded Krull domaingraded Noetherian ringpolynomial extension ring
주제분류수학

초록

Let R be a graded Noetherian domain and A a graded Krull overring of R. We show that if h-dim $R\leq2$, then A is a graded Noetherian domain with h-dim $A\leq2$. This is a generalization of the well-know theorem that a Krull overring of a Noetherian domain with dimension $\leq2$ is also a Noetherian domain with dimension $\leq2$.

Abstract

Let R be a graded Noetherian domain and A a graded Krull overring of R. We show that if h-dim $R\leq2$, then A is a graded Noetherian domain with h-dim $A\leq2$. This is a generalization of the well-know theorem that a Krull overring of a Noetherian domain with dimension $\leq2$ is also a Noetherian domain with dimension $\leq2$.

참고문헌 (9)

  1. D. D. Anderson, "Divisibility properties of graded domains", Canad. J. Math, 34(1), pp.196~215 (1982)
  2. R. Gilmer, "Commutative Semigroup Rings" (1984), University of Chicago Press
  3. W. Heinzer, "On Krull overrings of a Noetherian domain", Proc. Amer. Math. Soc, 22, pp.217~222 (1969)
  4. I. Kaplansky, "Commutative Rings" (1970), Allyn and Bacon
  5. H. Matsumura, "Commutative Ring Theory" (1986), Cambridge Univ. Press
  6. J. Nishimura, "Note on integral closures of a Noetherian integral domain", J. Math. Kyoto Univ, 16(1), pp.117~122 (1976)
  7. M. H. Park, "Integral closure of graded integral domains", Comm. Algebra, 35(12), pp.3965~3978 (2007)
  8. 박창환, "INTEGRAL CLOSURE OF A GRADED NOETHERIAN DOMAIN", 대한수학회지, 48(3), pp.449~464 (2011), 대한수학회
  9. D. E. Rush, "Noetherian properties in monoid rings", J. Pure Appl. Algebra, 185(1), pp.259~278 (2003)

관련 논문AI추천

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