A note on quasi-Buchsbaum rings
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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.References
- E. Graham Evans Jr. and Phillip A. Griffith, Local cohomology modules for normal domains, J. London Math. Soc. (2) 19 (1979), no. 2, 277–284. MR 533326, DOI 10.1112/jlms/s2-19.2.277
- Shiro Goto, Buchsbaum rings with multiplicity $2$, J. Algebra 74 (1982), no. 2, 494–508. MR 647250, DOI 10.1016/0021-8693(82)90035-7
- Shiro Goto, On Buchsbaum rings, J. Algebra 67 (1980), no. 2, 272–279. MR 602063, DOI 10.1016/0021-8693(80)90160-X
- Shiro Goto and Naoyoshi Suzuki, Index of reducibility of parameter ideals in a local ring, J. Algebra 87 (1984), no. 1, 53–88. MR 736769, DOI 10.1016/0021-8693(84)90160-1
- Bodo Renschuch, Jurgen Stückrad, and Wolfgang Vogel, Weitere Bemerkungen zu einem Problem der Schnittheorie und über ein Mass von A. Seidenberg für die Imperfektheit, J. Algebra 37 (1975), no. 3, 447–471 (German). MR 424799, DOI 10.1016/0021-8693(75)90070-8
- Jürgen Stückrad, Über die kohomologische Charakterisierung von Buchsbaum-Moduln, Math. Nachr. 95 (1980), 265–272 (German). MR 592900, DOI 10.1002/mana.19800950124
- Jürgen Stückrad and Wolfgang Vogel, Eine Verallgemeinerung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie, J. Math. Kyoto Univ. 13 (1973), 513–528 (German). MR 335504, DOI 10.1215/kjm/1250523322
- Jürgen Stückrad and Wolfgang Vogel, Toward a theory of Buchsbaum singularities, Amer. J. Math. 100 (1978), no. 4, 727–746. MR 509072, DOI 10.2307/2373908 N. Suzuki, On a basic theorem for quasi-Buchsbaum modules, Bull. Dept. General Ed. Shizuoka Coll. Pharmacy 11 (1982), 33-40.
- Wolfgang Vogel, A non-zero-divisor characterization of Buchsbaum modules, Michigan Math. J. 28 (1981), no. 2, 147–152. MR 616265 K. Yamagishi, On unconditioned strong $d$-sequences (to appear).
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