Let $K$ be a field and $x, y$ be independent variables. How can I show that $K(x, y)/K$ is not a simple extension?
Transcendental extension that is not simple
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abstract-algebra
field-theory
extension-field
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2Suppose to the contrary that it is simple and generated by some $t$. Write $x$ and $y$ as rational functions in $t$. Then show there is some relation between them, which contradicts independence. – 2012-06-15