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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on quasi-Buchsbaum rings


Author: Shiro Goto
Journal: Proc. Amer. Math. Soc. 90 (1984), 511-516
MSC: Primary 13H10; Secondary 13D03, 14B15
MathSciNet review: 733397
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Abstract: In this paper the ubiquity of non-Buchsbaum but quasi-Buchsbaum rings is established. The result is stated as follows: Let $ d \ge 3$ and $ {h_1},{h_2}, \ldots ,{h_{d - 1}} \ge 0$ be integers and assume that at least two of $ {h_i}$'s are positive. Then there exists a non-Buchsbaum but quasi-Buchsbaum local integral domain $ A$ of $ \dim A = d$ and such that $ {l_A}(H_m^i(A)) = {h_i}$ for all $ 1 \le i \le d - 1$. Moreover if $ {h_1} = 0$ the ring $ A$ can be chosen to be normal.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0733397-4
PII: S 0002-9939(1984)0733397-4
Keywords: Buchsbaum rings and modules, quasi-Buchsbaum rings and modules, local cohomology
Article copyright: © Copyright 1984 American Mathematical Society