Re: numeri algebrici

In article <1146852193.360406.222250@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
erg <mario.principato@xxxxxxxxxxxxx> wrote:
qualcuno mi sa dare una dimostrazione del seguente fatto :
il campo dei numeri algebrici =E8 algebricamente chiuso.

vorrei sapere come dimostrarlo.

Don't know if you know enough English, but:

If a is algebraic over the field of algebraic numbers, then there
exists a polynomial with algebraic number coefficients such that a
is a root. Let b_1,...,b_n be the coefficients. Then K=Q[b_1,...,b_n]
is finite over Q, and by assumption K(a) is finite over K, so K(a)
is finite over Q, hence a is algebraic over Q, hence a is in the
field of algebraic numbers.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

Quantcast