A Closed Formula for the Product in Simple Integral Extensions

Natalio H. Guersenzvaig; Fernando Szechtman

doi:10.1016/j.laa.2008.12.026

paper

A Closed Formula for the Product in Simple Integral Extensions

arXiv:1008.2163 · doi:10.1016/j.laa.2008.12.026

Abstract

Let $ξ$ be an algebraic number and let $α, β \in Q [ξ]$ . An explicit formula for the coordinates of the product $α β$ is given in terms of the coordinates of $α$ and $β$ and the companion matrix of the minimal polynomial of $ξ$ . The formula as well as its proof extend to fairly general simple integral extensions.