## Kyoto Journal of Mathematics

### Linear flags and Koszul filtrations

#### Abstract

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

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

Dates
Accepted: 7 May 2014
First available in Project Euclid: 9 September 2015

https://projecteuclid.org/euclid.kjm/1441824032

Digital Object Identifier
doi:10.1215/21562261-3089028

Mathematical Reviews number (MathSciNet)
MR3395974

Zentralblatt MATH identifier
1330.13011

#### Citation

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

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