# 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