Integral closures

Abstract

The q^th-power algorithm from Leonard [3], [4], and Leonard and Pellikaan [1] is a recent and efficient method of computing the integral closure of a ring in its field of fractions. Previously, the q^th-power algorithm has been used to compute integral closures over finite fields. In this dissertation, we use the q^th-power algorithm to compute integral closures over the rationals and number elds.