# Rings on $R^2$

by H. Holden (Gonzaga University)

Mathematics Magazine
February, 1989

Subject classification(s): Abstract Algebra
Applicable Course(s): 4.2 Mod Algebra I & II

How can we define multiplication of ordered pairs of real numbers to make $R^2$ into a ring, or field? In this article, the author derives conditions for certain types of rings and extends the results to $R^3$.

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