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The Arithmetic of Algebraic Numbers: An Elementary Approach

by Chi-Kwong Li (College of William and Mary) and David Lutzer (College of William and Mary)

This article originally appeared in:
College Mathematics Journal
September, 2004

Subject classification(s): Algebra and Number Theory
Applicable Course(s): 4.2 Mod Algebra I & II

If \(r\) and \(s\) are algebraic numbers, then \(r + s\), \(rs\), and \(r/s\) are also algebraic. The proof provided in this capsule uses the ideas of characteristic polynomials, eigenvalues, and eigenvectors.

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Capsule Course Topic(s):
Linear Algebra | Eigenvalues and Eigenvectors
Linear Algebra | Matrix Algebra
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