Re: a question about algebraic numbers

On Sun, 02 Apr 2006 18:00:34 EDT, Feng <lux@xxxxxxxxxxxx> wrote:

From others's post, I am considering a question, if a and b in C (complex numbers)are both algebraic, then what can we know about ab?
ab is also algebraic, that is obvious, anything else?
for example, is there any bound of the degree?

deg(ab) <= deg(a)*deg(b)

The degree of the product is bounded above by the product of the
degrees of the factors.

The proof is immediate -- just consider the chain of fields Q < Q(a) <
Q(a,b).

quasi
.