# Prove or disprove

• Nov 2nd 2009, 04:02 PM
dabien
Prove or disprove
Let a,b be elements which are algebraic over a field F, of degrees d,e respectively. The monomials a^i*b^j with i=0,...,d-1, j=0,...,e-1 form a basis of F(a,b) over F.
• Nov 2nd 2009, 04:30 PM
tonio
Quote:

Originally Posted by dabien
Let a,b be elements which are algebraic over a field F, of degrees d,e respectively. The monomials a^i*b^j with i=0,...,d-1, j=0,...,e-1 form a basis of F(a,b) over F.

$False.\,\, Take \,\,a=\sqrt{2}\,,\,\,b=-\sqrt{2}\,\,over\,\,\mathbb{Q}$

Tonio