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arXiv · 1008.2163

A Closed Formula for the Product in Simple Integral Extensions

Natalio H. Guersenzvaig·Fernando Szechtman
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Abstract

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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Natalio H. Guersenzvaig, Fernando Szechtman. 2010-08-07. A Closed Formula for the Product in Simple Integral Extensions. https://doi.org/10.1016/j.laa.2008.12.026

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