Embedded associated primes of powers of square-free monomial ideals

作者：Ha Huy Tai^*; Morey Susan

来源：Journal of Pure and Applied Algebra, 2010, 214(4): 301-308.

DOI：10.1016/j.jpaa.2009.05.002

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 beta(1), where beta(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 = beta(1) + 1. As an application, we investigate how these results relate to a conjecture of Conforti and Cornuejols.

• 出版日期2010-4