Vol. 64, No. 2, 1976

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Some results on normality of a graded ring

Wei-Eihn Kuan

Vol. 64 (1976), No. 2, 455–463

Let R = i0Ri be a graded domain and let p be a homogeneous prime ideal in R. Let Rp be the localization of R at p and R(p) = {ri∕si|risi Ri and sip}. If R1 (R p), then Rp is a localization of a transcendental extension of R(p). Thus Rp is normal (regular) if and only if R(p) is normal (regular). Let Proj(R) = {p|p is a homogeneous prime ideal and p i>0Ri}. Under certain conditions a Noetherian graded domain R is normal if R(p), is normal for each p Proj(R). If R = i0Ri is reduced and F0 = {ri∕ui|ri,ui Ri and ui U where U is the set of all nonzero divisors} is Noetherian, then the integral closure of R in the total quotient ring of R is also graded.

Mathematical Subject Classification 2000
Primary: 13A15
Received: 10 November 1975
Revised: 2 December 1975
Published: 1 June 1976
Wei-Eihn Kuan