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Homework Help: If F is algebraically closed, show Alg ext is closed too

  1. Apr 25, 2017 #1
    1. The problem statement, all variables and given/known data
    Let E be an algebraic extension of F in which every polynomial in F[x]
    can be factored into linear polynomials. Then E is algebraically closed.

    2. Relevant equations

    3. The attempt at a solution
    This seems like a very easy problem, but I'm not sure how to write things down formally.
  2. jcsd
  3. Apr 25, 2017 #2


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    2017 Award

    Staff: Mentor

    Start with the definition that you use: What is an algebraic closed field? What is an algebraic extension? How do they relate to F?

    That's why we have "2. Relevant equations" above. It's meant to tell us which definitions and notations you are used to. "This seems like a very easy problem" because it could well be the definition. Thus the question about your definition is the crucial part.
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