Date: Tue, 3 Mar 1998 11:08:30 -0500

From: Alex Bogomolny

Dear David:

Thank you for the kind words.

In the algebra of quaternions, the equation x^{2} + 1 = 0 has infinitely many solutions, not just 6: any x = ai + bj, where a^{2} + b^{2} = 1, satisfies the equation. So I would assume that the theory of algebraic equations on such an algebra is not very interesting.

I think the situation is analogous to the matrix algebra. Every square matrix satisfies its characteristic equation. But there are infinitely many matrices that share exactly same characteristic equation.

Best regards,

Alexander Bogomolny