English

A Closed Formula for the Product in Simple Integral Extensions

Rings and Algebras 2010-08-13 v1

Abstract

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

Keywords

Cite

@article{arxiv.1008.2163,
  title  = {A Closed Formula for the Product in Simple Integral Extensions},
  author = {Natalio H. Guersenzvaig and Fernando Szechtman},
  journal= {arXiv preprint arXiv:1008.2163},
  year   = {2010}
}
R2 v1 2026-06-21T16:00:07.063Z