At 12:45 +0400 98/08/04, S.D.Mechveliani wrote:
>Complexify(R) means to extend R algebraically with rootOf( x^2+1 ).
We are getting into a discussion of the usage of pure math terminology,
but I think that the complexification is normally just the tensor product I
indicated, whereas adjoining a root is something different (more difficult
to implement in a computer): If the ring R already contains an imaginary
unit, then the complexification still becomes the set of pairs r + i s, r,
s in R, with "i" a new formal unit, whereas when adjoining the root, the
rings stays the same.
So the complexification of the complex numbers have dimension four over
the real number, but when adjoining the root of x^2 + 1, the complex
numbers stay the same.
It is just a question of terminology, and not mathematics.
Hans Aberg
* Email: Hans Aberg <mailto:[EMAIL PROTECTED]>
* Home Page: <http://www.matematik.su.se/~haberg/>
* AMS member listing: <http://www.ams.org/cml/>
