Kyoto Journal of Mathematics

Linear flags and Koszul filtrations

Viviana Ene, Jürgen Herzog, and Takayuki Hibi

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1441824032

Digital Object Identifier
doi:10.1215/21562261-3089028

Mathematical Reviews number (MathSciNet)
MR3395974

Zentralblatt MATH identifier
1330.13011

Subjects
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

Keywords
Koszul filtrations linear flags K-algebra

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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References

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