INTEGRAL CLOSURE OF A GRADED NOETHERIAN DOMAIN
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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 ≤ n, and that if R is a graded Noetherian domain with h-dimR ≤ 2, then the integral closure R′ of R is also a graded Noetherian domain with h-dimR′ ≤ 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.
Abstract
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 ≤ n, and that if R is a graded Noetherian domain with h-dimR ≤ 2, then the integral closure R′ of R is also a graded Noetherian domain with h-dimR′ ≤ 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.
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