Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON GRADED KRULL OVERRINGS OF A GRADED NOETHERIAN DOMAIN

  • Received : 2010.10.20
  • Published : 2012.01.31
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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 $\leq2$.

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References

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  1. Graded integral domains in which each nonzero homogeneous t-ideal is divisorial pp.1793-6829, 2019, https://doi.org/10.1142/S021949881950018X
  2. Graded-Noetherian property in pullbacks of graded integral domains vol.67, pp.2, 2018, https://doi.org/10.1007/s11587-018-0357-0