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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cohen-Macaulay Section Rings

Author: Zhou Caijun
Journal: Trans. Amer. Math. Soc. 349 (1997), 4659-4667
MSC (1991): Primary 13C14, 13H10, 06A07
MathSciNet review: 1407695
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Abstract: In this paper, we study the section rings of sheaves of Cohen-Macaulay algebras (over a field $F$) on a ranked poset. A necessary and sufficient condition for these rings to be Cohen-Macaulay will be given. This is a further generalization of a result of Yuzvinsky, which generalizes Reisner's theorem concerning Stanley-Reisner rings.

References [Enhancements On Off] (What's this?)

  • [1] M. Auslander, D. A. Buchsbaum, Codimension and multiplicity, Ann. of Math. 68 (1958), 625-657. MR 20:6414
  • [2] K. Baclawski, Whitney numbers of geometric lattice, Adv. in Math. 16 (1975), 125-138. MR 52:7933
  • [3] K. Baclawski, Cohen-Macaulay ordered sets, J. Alg. 63 (1980), 226-258. MR 81m:06002
  • [4] R. Godement, Topologie alg$\acute {e}$brique et th$\acute {e}$orie des faisceaux, Hermann et cie, Paris, 1958. MR 21:1583
  • [5] H. Matsumura, Commutative Algebra, Benjamin Reading, MA, 1980. MR 82i:13003
  • [6] G. Reisner, Cohen-Macaulay quotients of polynomial rings, Adv. in Math. 21 (1976), 30-49. MR 53:10819
  • [7] R. Stanley, Combinatorics and Commutative Algebra, Birkhäuser, Boston, 1983. MR 85b:05002
  • [8] S. Yuzivinsky, Cohen-Macaulay rings of sections, Adv. in Math. 63 (1987), 172-195. MR 88d:13039
  • [9] S. Yuzivinsky, Flasque sheaves on posets and Cohen-Macaulay unions of regular varieties, Adv. in Math. 73 (1989), 24-42. MR 90a:13038

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Additional Information

Zhou Caijun
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received by editor(s): May 18, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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