From: rusin@washington.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Division algebras and other questions about products
Date: 13 Feb 1995 22:36:46 GMT

I previously announced a summary of the answers to a number of 
questions relating to product structures -- rings, division algebras,
quaternions, cross products, and so on. I received a number of very
helpful comments and corrections. The attempt to incorporate them
caused some substantial reorganization of the file. In particular, I
used to get my jollies knowing about an infinite number of division
algebras over the reals; since announcing the first summary I learned
from Daniel Shapiro there are many more. That's all in there now, as are
some other topics which seemed relevant. I'm still not done floating
around the library, but I'm sure I'll get comments advising revisions
of bibliographic citations anyway (thanks in advance). In the meantime
I think I'll not be broadcasting any significant falsehoods by posting
this URL: (gopher, FTP, and WWW should all work, after a fashion)
	ftp://math.niu.edu/pub/papers/Rusin/products/division.alg

The file runs about 59K (1000 lines).

Yes, this information will likely get folded into the regular FAQ once
y'all have given it the stamp of approval.

Here are the questions addressed:
Q1. Notation: what are rings, fields, algebras, and so on?
Q2. What is a domain? 
Q3. What is a division ring? division algebra? 
Q3a. What's an associative division ring?
Q3b. What's a non-associative division algebra?
Q4. How do you construct all the division algebras over the real numbers?
Q5. What's the question with answer "n=1, 2, 4, or 8"?
Q6. What makes the real numbers different? (Topology)
Q7. What can you say about finite rings?
Q8. Can you extend the cross product to  N  dimensions?
Q9. What's a Clifford algebra? exterior algebra?
Q10. How does this relate to projective geometry?
Q11. Can you extend the notion of quaternions?

Suggestion and comments are of course always welcome.

dave