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The Existence of Multiplicative Inverses

by Ricardo Alfaro (University of Michigan - Flint) and Steven Althoen (University of Michigan - Flint)

This article originally appeared in:
College Mathematics Journal
May, 2006

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

Using only basic ideas from linear algebra and number theory, the authors show that if \(c\) is square-free, the ring \(Q [\sqrt[n]{c}] \) is a field.


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