# The Existence of Multiplicative Inverses

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

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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