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.
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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.
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Originally Posted by dabien
$\displaystyle False.\,\, Take \,\,a=\sqrt{2}\,,\,\,b=-\sqrt{2}\,\,over\,\,\mathbb{Q}$
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