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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on quasi-Buchsbaum rings
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by Shiro Goto PDF
Proc. Amer. Math. Soc. 90 (1984), 511-516 Request permission

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
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 511-516
  • MSC: Primary 13H10; Secondary 13D03, 14B15
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0733397-4
  • MathSciNet review: 733397