Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Cohen-Macaulay Section Rings

Author(s): Zhou Caijun
Journal: Trans. Amer. Math. Soc. 349 (1997), 4659-4667.
MSC (1991): Primary 13C14, 13H10, 06A07
MathSciNet review: 1407695
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

[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

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 13C14, 13H10, 06A07

Retrieve articles in all Journals with MSC (1991): 13C14, 13H10, 06A07

Additional Information:

Zhou Caijun
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Email: shtunet@public.sta.net.cn

DOI: 10.1090/S0002-9947-97-01897-7
PII: S 0002-9947(97)01897-7
Received by editor(s): May 18, 1996
Copyright of article: Copyright 1997, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia