Show that Let K be an extension of a field F and a e K be algebraic over F. Then F[a] = F (a), where F[a] = {f (a) : f (x) e F [x]}.
Show that Let K be an extension of a field F and a e K be algebraic over F. Then F[a] = F (a), where F[a] = {f (a) : f (x) e F [x]}.
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Proof
![Show that Let K be an extension of a field F and a e K be
algebraic over F. Then
F[a] = F (a), where F[a] = {f (a) : f (x) e F [x]}.
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Transcribed Image Text:Show that Let K be an extension of a field F and a e K be
algebraic over F. Then
F[a] = F (a), where F[a] = {f (a) : f (x) e F [x]}.
%3D
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