Kyoto Journal of Mathematics

Linear flags and Koszul filtrations

Viviana Ene, Jürgen Herzog, and Takayuki Hibi

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We show that the graded maximal ideal of a graded K-algebra R has linear quotients for a suitable choice and order of its generators if the defining ideal of R has a quadratic Gröbner basis with respect to the reverse lexicographic order, and we show that this linear quotient property for algebras defined by binomial edge ideals characterizes closed graphs. Furthermore, for algebras defined by binomial edge ideals attached to a closed graph and for join-meet rings attached to a finite distributive lattice we present explicit Koszul filtrations.

Article information

Kyoto J. Math., Volume 55, Number 3 (2015), 517-530.

Received: 9 December 2013
Accepted: 7 May 2014
First available in Project Euclid: 9 September 2015

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Primary: 13C13: Other special types 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13F99: None of the above, but in this section 05E40: Combinatorial aspects of commutative algebra

Koszul filtrations linear flags K-algebra


Ene, Viviana; Herzog, Jürgen; Hibi, Takayuki. Linear flags and Koszul filtrations. Kyoto J. Math. 55 (2015), no. 3, 517--530. doi:10.1215/21562261-3089028.

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  • [1] A. Conca, Universally Koszul algebras, Math. Ann. 317 (2000), 329–346.
  • [2] A. Conca, M. E. Rossi, and G. Valla, Gröbner flags and Gorenstein algebras, Compos. Math. 129 (2001), 95–121.
  • [3] A. Conca, N. V. Trung, and G. Valla, Koszul property for points in projective spaces, Math. Scand. 89 (2001), 201–216.
  • [4] D. A. Cox and A. Erskine, On closed graphs, I, preprint, arXiv:1306.5149v2 [math.CO].
  • [5] V. Ene, J. Herzog, and T. Hibi, Cohen-Macaulay binomial edge ideals, Nagoya Math. J. 204 (2011), 57–68.
  • [6] V. Ene, J, Herzog, and T. Hibi, “Koszul binomial edge ideals” in Bridging Algebra, Geometry, and Topology, Springer Proc. Math. Stat. 96, Springer, Cham, 2014, 125–136.
  • [7] J. Herzog and T. Hibi, Monomial Ideals, Grad. Texts in Math. 260, Springer, London, 2010.
  • [8] J. Herzog, T. Hibi, F. Hreinsdóttir, T. Kahle, and J. Rauh, Binomial edge ideals and conditional independence statements, Adv. in Appl. Math. 45 (2010), 317–333.
  • [9] J. Herzog, T. Hibi, and G. Restuccia, Strongly Koszul algebra, Math. Scand. 86 (2000), 161–178.
  • [10] T. Hibi, A. A. Qureshi, and A. Shikama, A Koszul filtration for the second squarefree Veronese subring, Int. J. Algebra 9 (2015), 7–14.
  • [11] H. Ohsugi and T. Hibi, Toric ideals generated by quadratic binomials, J. Algebra 218 (1999), 509–527.
  • [12] M. Ohtani, Graphs and ideals generated by some $2$-minors, Comm. Algebra 39 (2011), 905–917.
  • [13] J.-E. Roos, Commutative non-Koszul algebras having a linear resolution of arbitrarily high order. Applications to torsion in loop space homology, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 1123–1128.
  • [14] B. Sturmfels, Gröbner Bases and Convex Polytopes, Univ. Lecture Ser. 8, Amer. Math. Soc., Providence, 1995.