Re: Algebraic Extension
- From: Kira Yamato <kirakun@xxxxxxxxxxxxx>
- Date: Wed, 07 Sep 2005 02:38:02 GMT
On Tue, 06 Sep 2005 21:29:34 -0400, Simon Dean wrote:
> Could someone please explain to me why Q subset of Q( 2^(1/2), 2^(1/3),...) is an algebraic extension but not finitely generated. (Here Q represents the rational numbers)
>
> Thanks in advance,
> Simon
Minimum polynomial for 2^{1/n} is x^n-2. So [Q(2^{1/n}):Q]=n. Since
Q(2^{1/n}) is a subfield of Q(...) and n is arbitrary, the extension can't
be finite.
-kira
.
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- Algebraic Extension
- From: Simon Dean
- Algebraic Extension
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