Isomorphisms Described
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f(x)=x^3+x+1 and g(x)=x^3+x^2+1 are irreducible over F_2. K is the field extension obtained by adjoining a root of f and L is the extension obtained by adjoining a root of g. Determine the number of isomorphisms from K to L. (It is not necessary to explicitly describe such an isomorphism)
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The expert determines the number of isomorphism from K to L.
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f(x)=x^3+x+1 and g(x)=x^3+x^2+1 are irreducible over F_2. K is the field extension obtained by adjoining a root of f and L is the extension obtained by adjoining a root of g. Determine the number of isomorphisms from K to L. (It is not necessary to explicitly describe such an isomorphism)
Solution: Let K=F_2 (α), where α is a root of f(x)=x^3+x+1.
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