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http://dx.doi.org/10.4134/JKMS.2011.48.3.449

INTEGRAL CLOSURE OF A GRADED NOETHERIAN DOMAIN  

Park, Chang-Hwan (Department of Mathematics Chung-Ang University)
Park, Mi-Hee (Department of Mathematics Chung-Ang University)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.3, 2011 , pp. 449-464 More about this Journal
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 ${\leq}$ n, and that if R is a graded Noetherian domain with h-dim R ${\leq}$ 2, then the integral closure R' of R is also a graded Noetherian domain with 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;
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