# 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)

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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