Bulletin of the
Korean Mathematical Society BKMS

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