Geodesic
A Note on Buchsbaum Rings and Localizations of Graded Domains
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1244-1249

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Let R = ⊕i ≧0R i be a graded integral domain, and let p ∈ Proj (R) be a homogeneous, relevant prime ideal. Let R(P) = {r/t| r ∈ R i , t ∈ R i \p}be the geometric local ring at p and let R p = {r/t| r ∈ R, t ∈ R\p} be the arithmetic local ring at p. Under the mild restriction that there exists an element r 1 ∈ R 1\p, W. E. Kuan [2], Theorem 2, showed that r 1 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. 
Daepp, U.; Evans, A. A Note on Buchsbaum Rings and Localizations of Graded Domains. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1244-1249. doi: 10.4153/CJM-1980-092-6
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