Let K be a field with characteristic p > 0 and M = K ( X ,

Dayanara Terry

Dayanara Terry

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Let K be a field with characteristic p > 0 and M = K ( X , Y ) the field of rational functions in 2 variables over K. We consider the subfield L = K ( X p , Y p )  M.
Show that [ M : L ] = p 2 .
We need the property that [ K ( x ) : K ( x n ) ] = n, which we showed already. But I actually do not know how to use it here. I can not work well with that field in 2 variables..

Answer & Explanation



Beginner2022-06-30Added 13 answers

Keep in mind that in some fields J so that L  J  M You are in possession of the extension's degree L  M is calculated as the product of the extensions' degrees. L  J and J  M.
Use this for example with J = K ( X p , Y ), applying the outcome you are aware of twice.

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