A Closed Formula for the Product in Simple Integral Extensions

Details A Closed Formula for the Product in Simple Integral Extensions A Closed Formula for the Product in Simple Integral Extensions

2010-08-07

arxiv.org/abs/1008.2163v1

Linear Algebra and its Applications 430 (2009) 2464-2466

Mathematics

Rings and Algebras

Scientific paper

10.1016/j.laa.2008.12.026

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

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