Field extension Question?



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Let E=F(a,b), a , b are elmenets in E. And a and b is algebraic over F where [F(a):F]=m and [F(b):F]=n. THen why

[F(a,b):F(b)]<=[F(a):F]=m

I have another question. If b is in F(a), then is F(a,b) = F(a) since as i understand, F(a) is a field and it contain b, so F(a,b) will then be the field containing a, b and F. Am i right?

Field extension Question?opera cd

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