Embedded associated primes of powers of square-free monomial ideals |
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Authors: | Huy Tài Hà Susan Morey |
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Institution: | a Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, LA 70118, United States b Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666, United States |
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Abstract: | An ideal I in a Noetherian ring R is normally torsion-free if Ass(R/It)=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 It has embedded primes is bigger than β1, where β1 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 It do occur when t=β1+1. As an application, we investigate how these results relate to a conjecture of Conforti and Cornuéjols. |
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Keywords: | 13A17 13F55 05C65 90C27 |
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