A Note on Buchsbaum Rings and Localizations of Graded Domains
1980 ◽
Vol 32
(5)
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pp. 1244-1249
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Keyword(s):
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) andwhere 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.
1980 ◽
Vol 32
(5)
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pp. 1261-1265
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2019 ◽
Vol 19
(02)
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pp. 2050033
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2020 ◽
Vol 2
(2)
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pp. 183
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2019 ◽
Vol 19
(04)
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pp. 2050061
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1982 ◽
Vol 91
(2)
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pp. 207-213
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2019 ◽
Vol 18
(01)
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pp. 1950018
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Keyword(s):
1984 ◽
Vol 25
(1)
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pp. 27-30
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