An Algorithm for Computing the Integral Closure

We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field. Leonard and Pellikaan [4] devised an algorithm for computing the integral closure of weighted rings that are finitely generated over finite fields. Previous algorithms proceed by building successively larger rings between the original ring and its integral closure, [2, 6, 7, 9, 11, 12]. The LeonardPellikaan algorithm instead starts with the first approximation being a finitely generated module that contains the integral closure, and successive steps produce submodules containing the integral closure. The weights in [4] impose strong restrictions; these weights play a crucial role in all steps of their algorithm. We present a modification of the Leonard-Pellikaan algorithm which works in much greater generality: it computes the integral closure of a reduced ring that is finitely generated over a finite field. We discuss an implementation of the algorit...

• Type: Journal
• Year: 1998
• Where: JSC
• Authors: Theo De Jong
• Keywords: Algorithm, Integral Closure, JSC 1998, finite field