ON GRADED KRULL OVERRINGS OF A GRADED NOETHERIAN DOMAIN

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 $\leq2$.

Keywords

• graded Noetherian ring;
• graded Krull domain;
• polynomial extension ring

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References

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Cited by

1. Graded integral domains in which each nonzero homogeneous t-ideal is divisorial pp.1793-6829, 2018, 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