page1950 Rings Matthias Lorentzen...mattegrisenforlag.com
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Question
In the proof that `beta` is algebraic over `F(alpha)`, why
is it essential that `beta` is transcendental over F:
A) If `beta` were algebraic over F, transitivity would
force `alpha` to be algebraic over F, contradicting `alpha's`
given transcendence.
B) If `beta` were algebraic over F, the field `F(beta)` would
not contain rational functions needed to define the polynomial
p(x)
?
