Nagoya Mathematical Journal

Shellability of semigroup rings

Annetta Aramova, Jürgen Herzog, and Takayuki Hibi

Full-text: Open access

Abstract

The concepts of $\Lambda$-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 $\Lambda$-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.

Article information

Source
Nagoya Math. J., Volume 168 (2002), 65-84.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631780

Mathematical Reviews number (MathSciNet)
MR1942394

Zentralblatt MATH identifier
1041.16018

Subjects
Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Secondary: 13F50: Rings with straightening laws, Hodge algebras 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]

Citation

Aramova, Annetta; Herzog, Jürgen; Hibi, Takayuki. Shellability of semigroup rings. Nagoya Math. J. 168 (2002), 65--84. https://projecteuclid.org/euclid.nmj/1114631780


Export citation

References

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