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Math Help - Prove or disprove

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by dabien View Post
    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}

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