Journal of the
Korean Mathematical Society JKMS

We show that, if $R$ is a graded Noetherian ring and $I$ is a proper ideal of $R$ generated by $n$ homogeneous elements, then any prime ideal of $R$ minimal over $I$ has h-height $\leq n$, and that if $R$ is a graded Noetherian domain with $\text{h-dim}\,R\leq 2$, then the integral closure $R'$ of $R$ is also a graded Noetherian domain with $\text{h-dim}\,R'\leq 2$. We also present a short improved proof of the result that, if $R$ is a graded Noetherian domain, then the integral closure of $R$ is a graded Krull domain.

Keywords: graded ring, graded module, Noetherian ring, Krull domain, integral closure

MSC numbers: 13A02, 13A15, 13B22, 13E05, 13F05