Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 55, Number 3 (2015), 517-530.
Linear flags and Koszul filtrations
We show that the graded maximal ideal of a graded -algebra has linear quotients for a suitable choice and order of its generators if the defining ideal of 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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. https://projecteuclid.org/euclid.kjm/1441824032