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Product Structures and Division Rings over the Real Numbers

Here's a long summary of answers to questions frequently asked in the sci.math newsgroup concerning products on R^n, especially cross products, and a general review of algebras and (more generally) rings. In particular, we address the question of what division algebras are, and give the answer "1, 2, 4, 8".

These issues are really just part of ring theory ( commutative, associative (noncommutative), or nonassociative) The special role played by the real numbers introduces connections with topology; in particular, the non-existence of division algebras of high dimension was proven using facts about spheres; a FAQ on spheres is a separate page.

This is the division algebra FAQ itself.

I've also saved a few other letters and posts which may be relevant:

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Last modified 2000/01/17 by Dave Rusin. Mail: