Journal of Commutative Algebra

Rees algebras of square-free monomial ideals

Louiza Fouli and Kuei-Nuan Lin

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We determine the defining equations of the Rees algebra of an ideal $I$ in the case where $I$ is a square-free monomial ideal such that each connected component of the line graph of the hypergraph corresponding to $I$ has at most $5$ vertices. Moreover, we show in this case that the non-linear equations arise from even closed walks of the line graph, and we also give a description of the defining ideal of the toric ring when $I$ is generated by square-free monomials of the same degree. Furthermore, we provide a new class of ideals of linear type. We show that when $I$ is a square-free monomial ideal with any number of generators and the line graph of the hypergraph corresponding to $I$ is the graph of a disjoint union of trees and graphs with a unique odd cycle, then $I$ is an ideal of linear type.

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J. Commut. Algebra, Volume 7, Number 1 (2015), 25-53.

First available in Project Euclid: 2 March 2015

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Primary: 13A02: Graded rings [See also 16W50] 13A15: Ideals; multiplicative ideal theory 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 05C05: Trees 05E40: Combinatorial aspects of commutative algebra 05E45: Combinatorial aspects of simplicial complexes

Rees algebras square-free monomial ideals relation type ideals of linear type graph


Fouli, Louiza; Lin, Kuei-Nuan. Rees algebras of square-free monomial ideals. J. Commut. Algebra 7 (2015), no. 1, 25--53. doi:10.1216/JCA-2015-7-1-25.

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