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  1. S

    MHB Prove F(a,b)=F(a)(b)=F(b)(a) in Field Extensions

    Yes
  2. S

    MHB Prove F(a,b)=F(a)(b)=F(b)(a) in Field Extensions

    Let E be an extension of F and let a, b belong to E. Prove that F(a,b) =F(a)(b) = F(b)(a).
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    MHB Roots of an irreducible polynomial over a finite field

    Let F=Z2 and let f(x) = X^3 +x+1 belong to F[x]. Suppose that a is a zero of f(x) in some extension of F. Using the field created above F(a) Show that a^2 and a^2+a are zeros of x^3+x+1?
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