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The monomial ideal of a finite meet-semilattice
Author(s):
Jürgen
Herzog;
Takayuki
Hibi;
Xinxian
Zheng
Journal:
Trans. Amer. Math. Soc.
358
(2006),
4119-4134.
MSC (2000):
Primary 13D02, 13H10, 06A12, 06D99
Posted:
February 20, 2006
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Abstract:
Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice, the Alexander dual is computed.
References:
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- D. Bayer and B. Sturmfels, Cellular resolutions of monomial modules, J. Reine Angew. Math. 502 (1998), 123-140. MR 1647559 (99g:13018)
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- W. Bruns and J. Herzog, ``Cohen-Macaulay rings,'' Revised Edition, Cambridge University Press, 1996. MR 1251956 (95h:13020)
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- J. Eagon and V. Reiner, Resolutions of Stanley-Reisner rings and Alexander duality, J. Pure Appl. Algebra 130 (1998), 265-275.MR 1633767 (99h:13017)
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- P. Edelman, Abstract convexity and meet-distributive lattices, in ``Combinatorics and ordered sets'' (Arcata, Calif., 1985), Contemp. Math. 57, 127-150, Amer. Math. Soc., Providence, RI, 1986. MR 0856235 (87m:52003)
- 5.
- D. Eisenbud, ``Commutative Algebra with a view to Algebraic geometry'', Springer-Verlag, 1995. MR 1322960 (97a:13001)
- 6.
- J. Herzog and T. Hibi, Distributive Lattices, Bipartite Graphs and Alexander Duality, J. Alg. Combin. 22 (2005), 289-303. MR 2181367
- 7.
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- 8.
- T. Hibi, Distributive lattices, affine semigroup rings and algebras with straightening laws, in ``Commutative Algebra and Combinatorics'' (M. Nagata and H. Matsumura, Eds.), Advanced Studies in Pure Math., Volume 11, North-Holland, Amsterdam, 1987, pp. 93-109.MR 0951198 (90b:13024)
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Additional Information:
Jürgen
Herzog
Affiliation:
Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, 45117 Essen, Germany
Email:
juergen.herzog@uni-essen.de
Takayuki
Hibi
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email:
hibi@math.sci.osaka-u.ac.jp
Xinxian
Zheng
Affiliation:
Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, 45117 Essen, Germany
Email:
xinxian.zheng@uni-essen.de
DOI:
10.1090/S0002-9947-06-03842-6
PII:
S 0002-9947(06)03842-6
Received by editor(s):
November 6, 2003
Received by editor(s) in revised form:
September 2, 2004 and September 9, 2004
Posted:
February 20, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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