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Math Help - extension of a field

  1. #1
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    extension of a field

    Prove: Let E be a finite extension of a field F. Let F₁ and F₂ be subfields of E containing F. Then F₁+F₂ is not a subfield of E, except in the cases when F₁ is subset of F₂ or F₂ is subset of F₁.
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  2. #2
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    Quote Originally Posted by apple2009 View Post
    Prove: Let E be a finite extension of a field F. Let F₁ and F₂ be subfields of E containing F. Then F₁+F₂ is not a subfield of E, except in the cases when F₁ is subset of F₂ or F₂ is subset of F₁.


    Suppose F_1\nsubseteq F_2 \,,\,F_2\nsubseteq F_1\Longrightarrow \exists f_1\in F_1-F_2\,,\,\exists f_2\in F_2-F_1 . Now the question is: where does f_1+f_2 belong to?

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