The koszul property in affine semigroup rings

Pacific Journal of Mathematics

Volumn 186, Issue 1, 1998, Pages 39-65

  Herzog, Jürgen ^a   Reiner, Vic ^b   Welker, Volkmar ^c  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b UNIVERSITY OF MINNESOTA   (United States)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001771256     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1998.186.39     Document Type: Article

References (25)

1. S.S. Abhyankar, Local rings of high embedding dimension, Amer. J. Math., 83 (1967), 1073-1077.
2. J. Backelin and R. Fröberg, Poincaré series of short Artinian rings, J. Algebra, 96 (1985), 495-498.
3. A. Björner, A. Garsia and R. Stanley, An introduction to Cohen-Macaulay partially ordered sets, in 'Ordered sets' (Banff, Alberta 1981), NATO-Reidel/Dordrecht, Boston, (1982), 583-615.
4. A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, 304, Springer-Verlag, Berlin, 1972.
5. W. Bruns and J. Herzog, Cohen-Macualay Rings, Cambridge University Press, 1993.
6. _, Semigroup rings and simplicial complexes, J. Pure Appl. Algebra, 122 (1997), 185-208.
7. W. Bruns, J. Herzog and U. Vetter, Syzygies and walks, Commutative Algebra, World Scientific, (1994), 36-57.
8. P. Cartier and D. Foata, Problèmes combinatoire des commutations et réarrangements, Lecture Notes in Mathematics, 85, Springer, Heidelberg, 1969.
9. D. Cox, J. Little and D. O'Shea, Ideals, varieties, and algorithms: An introduction to computational algebraic geometry and commutative algebra, Springer-Verlag, New York, 1997.
10. G. Danaraj and V. Klee, Shellings of spheres and polytopes, Duke Math. J., 41 (1974), 443-451.
11. D. Eisenbud, Commutative Algebra with a View Towards Algebraic Geometry, Springer Verlag, New York, 1995.
12. R. Fröberg, Determination of a class of Poincaré series, Math. Scand., 37 (1975), 29-39.
13. _, Connections between a local ring and its associated graded ring, J. Algebra, 111 (1987), 300-305.
14. I.M. Gelfand, M.M. Kapranov and A.V. Zelevinsky, Discriminants, Resultants and Multidimensional Determinants, Birkhäuser, Boston, 1994.
15. C. Greene and T. Zaslavsky, On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-radon partitions, and orientations of graphs, Trans. Amer. Math. Soc., 280 (1983), 97-125.
16. O.A. Laudal and A. Sletsjøe, Betti numbers of monoid algebras. Applications to 2-dimensional torus embeddings, Math. Scand., 56 (1985), 145-162.
17. S. Mac Lane, Homology, Springer-Verlag, 1975.
18. P. Orlik and H. Terao, Arrangements of Hyperplanes, Springer-Verlang, 1992.
19. I. Peeva, V. Reiner and B. Sturmfels, How to shell a monoid, Math. Ann., 3b (1998), 379-393.
20. D. Quillen, Homotopy properties of the poset of nontrivial p-subgroups of a group, Adv. in Math., 28(2) (1978), 101-128.
21. J.D. Sally, On the associated graded ring of a local Cohen-Macaulay ring, J. Math. Kyoto U., 17 (1977), 19-21.
22. R.P. Stanley, Enumerative Combinatorics, I, Wadsworth & Brooks/Cole, Monterey, CA, 1986.
23. M. Wachs, Whitney homology of semipure shellable posets, preprint, July 1996.
24. V. Welker, G.M. Ziegler and R. Živaljević, Comparison lemmas and applications for diagrams of spaces, submitted, preprint, 1995.
25. G.M. Ziegler and R. Živaljević, Homotopy types of subspace arrangements via diagrams of spaces, Math. Ann., 295 (1993), 527-548.