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Rings on \(R^2\)

by H. Holden (Gonzaga University)

This article originally appeared in:
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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