Let $E/F$ be a finite separable extension, and let $K$ be a function field with constant field $F$. Is the compositum $KE$ of $K$ and $E$ a separable extension over $E$?
Separability of compositum of fields
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field-theory
function-fields
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0Does it really make sense to talk about separability here? It doesn't look like $KE/E$ is going to be algebraic. – 2012-03-01
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0@DylanMoreland: the separability over $E$ can be defined for any $E$-algebra $A$. It means $A\otimes_E B$ is reduced for any reduced $E$-algebra $B$ (equivalently, $B=$ the algebraic closure of $E$). – 2012-03-01
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1@QiL Thanks, that makes sense. [If you are who I think you are: I love your book!] – 2012-03-01
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0@DylanMoreland: thanks ! – 2012-03-04