Embedded Associated Primes of Powers of Square-free Monomial Ideals

By Huy Tài Hà, Susan Morey. 2008

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Abstract An ideal I in a Noetherian ring R is normally torsion-free if Ass ( R / I t ) = Ass ( R / I ) for all t ≥ 1 . We develop a technique to inductively study normally torsion-free square-free monomial ideals. In particular, we show that if a square-free monomial ideal I is minimally not normally torsion-free then the least power t such that I t has embedded primes is bigger than β 1 , where β 1 is the monomial grade of I , which is equal to the matching number of the hypergraph H ( I ) associated to I . If, in addition, I fails to have the packing property, then embedded primes of I t do occur when t = β 1 + 1 . As an application, we investigate how these results relate to a conjecture of Conforti and Cornuejols.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1bb3d7460bacab684037ee83a310a3d88887eaaa

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Citations in the corpus

Depths of Powers of the Edge Ideal of a Tree (2009, background): “In particular, by [4] min depth R/It ≤ n− I where I is the analytic spread of I , and the minimum is taken over all powers t.”
Edge ideals: algebraic and combinatorial properties (2010, background): “, Cohen-Macaulayness, unmixedness, normality, normally torsion-freeness, shellability, vertex decomposability, stability of associated primes) is of current interest, see [22, 24, 25, 32, 39, 40, 41, 45, 51, 61, 62, 89, 116] and the references there.”