Let F be an extension field of K. Let a ∈ F be algebraic over K, and let t ∈ F be transcendental over K. Show that a+t is transcendental over K.
I am completely lost. Can anyone help at all? Thanks!
Follow Math Help Forum on Facebook and Google+
Use a proof by contradiction. Let x= a+ t. If x is NOT transcendental, it satisfies some polynomial equation, P(x)= 0, with coefficients in K. Then P(a+ t)= 0.
View Tag Cloud