Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-09T18:49:57.382Z Has data issue: false hasContentIssue false
  • English
  • Français

Shellability of semigroup rings

Published online by Cambridge University Press:  22 January 2016

Annetta Aramova ,
Jürgen Herzog  and
Takayuki Hibi
Annetta Aramova
Affiliation:
FB6 Mathematik und Informatik, Universität – GHS – Essen, Postfach 103764, 45117 Essen, Germany, A.Aramova@uni-essen.de
Jürgen Herzog
Affiliation:
FB6 Mathematik und Informatik, Universität – GHS – Essen, Postfach 103764, 45117 Essen, Germany, juergen.herzog@uni-essen.de
Takayuki Hibi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan, hibi@math.sci.osaka-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The concepts of Λ-shellability of locally finite posets as well as of extendable sequentially Koszul algebras will be introduced. It will be proved that the divisor poset of a homogeneous semigroup ring is Λ-shellable if and only if the semigroup ring is extendable sequentially Koszul. Examples of extendable sequentially Koszul semigroup rings contain all monomial ASL’s (algebras with straightening laws) and all second squarefree Veronese subrings.

Keywords

13H1013F5013F55

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 168 , 2002 , pp. 65 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Björner, A., Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc., 260 (1980), 159–183.CrossRefGoogle Scholar
[2] Björner, A. and Wachs, M., On lexicographically shellable posets, Trans. Amer. Math. Soc., 277 (1983), 323–341.Google Scholar
[3] Bruns, W. and Herzog, J., Cohen-Macaulay Rings, Cambridge University Press, Cambridge, New York, Sydney, 1993.Google Scholar
[4] Eisenbud, D., Introduction to algebras with straightening laws, Ring Theory and Algebra III (B. R. McDonald, ed.), Dekker, New York (1980), pp. 243–268.Google Scholar
[5] Herzog, J., Hibi, T. and Restuccia, G., Strongly Koszul algebras, Math. Scand., 86 (2000), 161–178.Google Scholar
[6] Herzog, J., Reiner, V. and Welker, V., The Koszul property in affine semigroup rings, Pacific J. Math., 186 (1998), 39–65.Google Scholar
[7] Hibi, T., Algebraic Combinatorics on Convex Polytopes, Carslaw Publications, Glebe, N.S.W., Australia, 1992.Google Scholar
[8] Ohsugi, H., Herzog, J. and Hibi, T., Combinatorial pure subrings, Osaka J. Math., 37 (2000), 745–757.Google Scholar
[9] Ohsugi, H. and Hibi, T., Toric ideals generated by quadratic binomials, Algebra J., 218 (1999), 509–527.Google Scholar
[10] Ohsugi, H. and Hibi, T., Compressed polytopes, initial ideals and complete multipartite graphs, Illinois J. Math., 44 (2000), 391–406.Google Scholar
[11] Peeva, I., Reiner, V. and Sturmfels, B., How to shell a monoid, Math. Ann., 310 (1998), 379–393.CrossRefGoogle Scholar
[12] Stanley, R., Enumerative Combinatorics, Volume I, Wadsworth & Brooks/Cole, Monterey, Calif., 1986.Google Scholar
[13] Sturmfels, B., Gröbner Bases and Convex Polytopes, Amer. Math. Soc., Providence, RI, 1995.Google Scholar