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A Note on Buchsbaum Rings and Localizations of Graded Domains

Published online by Cambridge University Press:  20 November 2018

U. Daepp  and
A. Evans
U. Daepp
Affiliation:
Michigan State University, East Lansing, Michigan
A. Evans
Affiliation:
Vassar College, Poughkeepsie, New York
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Let R = ⊕i ≧0Ri be a graded integral domain, and let p ∈ Proj (R) be a homogeneous, relevant prime ideal. Let R(P) = {r/t| r ∈ Ri, t ∈ Ri\p} be the geometric local ring at p and let Rp = {r/t| r ∈ R, t ∈ R\p} be the arithmetic local ring at p. Under the mild restriction that there exists an element r1 ∈ R1\p, W. E. Kuan [2], Theorem 2, showed that r1 is transcendental over R(P) and

where S is the multiplicative system R\p. It is also demonstrated in [2] that R(P) is normal (regular) if and only if Rp is normal (regular). By looking more closely at the relationship between R(P) and R(P), we extend this result to Cohen-Macaulay (abbreviated C M.) and Gorenstein rings.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 5 , 01 October 1980 , pp. 1244 - 1249
Copyright
Copyright © Canadian Mathematical Society 1980

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