The February 18, 2014 O.M.N.I. Talk: William Taylor presents

Integral Closure of Ideals

Abstract: In a natural analogue to the concept of integral closure of ring extensions, we have in algebra a concept of integral closure of ideals. In this talk we will define what it means for an element of a ring to be integral over an ideal in that ring. We will give several characterizations of integral closure in general. Finally, we will prove a remarkable relationship between the integral closure of a monomial ideal in a polynomial ring and the Newton polyhedron associated to that ideal.