Commutative Algebra and its Interactions A conference in honor of Mel Hochster July 31 - August 5, 2008 Abstract Detail   Title: Integral closure This is joint work with Anurag Singh. I will present the history of the computation of integral closures, starting with Dedekind's determination of the integral closures of cyclic extensions of the ring of integers, and ending with our recent joint work. I will concentrate mostly on the algorithmic aspects of the computation. The first algorithmic consideration is due to Stolzenberg from 1975, and was improved by Seidenberg. A more effective method for computing the integral closure of affine domains is due to Grauert, Remmert, and de Jong, and further modifications and refinements are due to Vasconcelos. These algorithms successively approximate the integral closure from below, namely by building successively strictly larger rings between the original ring and its integral closure. Based on a specialized 2003 algorithm of Leonard--Pellikaan, we prove a more general version of the construction of the integral closure that starts instead with a finitely generated module over the ring that contains the integral closure, and the successive steps produce strictly smaller submodules that contain the integral closure. Irena Swanson Reed College Email:  iswanson@reed.edu Phone: 503 517 7399   BACK to Speaker Listing BACK to Conference Home