On graded Krull overrings of a graded Noetherian domain
Bull. Korean Math. Soc. 2012 Vol. 49, No. 1, 205-211
https://doi.org/10.4134/BKMS.2012.49.1.205
Published online January 1, 2012
Eun Kyung Lee and Mi Hee Park
Chung-Ang University, Chung-Ang University
Abstract : Let $R$ be a graded Noetherian domain and $A$ a graded Krull overring of $R$. We show that if $\text{h-dim}\, R\leq 2$, then $A$ is a graded Noetherian domain with $\text{h-dim}\, A\leq 2$. This is a generalization of the well-known theorem that a Krull overring of a Noetherian domain with dimension $\leq 2$ is also a Noetherian domain with dimension $\leq 2$.
Keywords : graded Noetherian ring, graded Krull domain, polynomial extension ring
MSC numbers : 13A02, 13B25, 13E05, 13F05
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