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SPRING 2015 Rees algebras of square-free monomial ideals
Louiza Fouli, Kuei-Nuan Lin
J. Commut. Algebra 7(1): 25-53 (SPRING 2015). DOI: 10.1216/JCA-2015-7-1-25

Abstract

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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Louiza Fouli. Kuei-Nuan Lin. "Rees algebras of square-free monomial ideals." J. Commut. Algebra 7 (1) 25 - 53, SPRING 2015. https://doi.org/10.1216/JCA-2015-7-1-25

Information

Published: SPRING 2015
First available in Project Euclid: 2 March 2015

zbMATH: 1310.13008
MathSciNet: MR3316984
Digital Object Identifier: 10.1216/JCA-2015-7-1-25

Subjects:
Primary: 05C05, 05E40, 05E45, 13A02, 13A15, 13A30

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.7 • No. 1 • SPRING 2015
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