Hello Martin,

> I am therefore looking for another way to combine these algebras in
> interesting ways.

If you look at real Clifford algebras, and within them at spinor
modules (vector spaces)
then you can model all of the required number systems as sub Clifford
alegbras. So
if that is your only venue you need only Clifford algebras over
Clifford numbers.

> zeros of x^2+1, but I can't think how polynomials could represent dual
> or double numbers and so on?

What about R[x]/<x^2> and R[x]/<x^2-1> ?

Sorry for being short,
Cheers
BF.


-- 
% PD Dr Bertfried Fauser
%       Research Fellow, School of Computer Science, Univ. of Birmingham
%       Honorary Associate, University of Tasmania
%       Privat Docent: University of Konstanz, Physics Dept
<http://www.uni-konstanz.de>
% contact |->    URL : http://www.cs.bham.ac.uk/~fauserb/
%              Phone :  +44-121-41-42795

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