For my master thesis, I need to examine the following statement:
$Frac(R) \otimes_{k} L \cong Frac(R \otimes_{k} L)$, where $R$ is an integral domain over the perfect field $k$ and $L$ is a finite field extension of $k$.
My first idea was to write: $L = k(y)$ and $Frac(R) \otimes_{k} L = Frac(R)(y)$, $Frac(R \otimes_{k} L) = Frac(R(y))$. If $R[y]$ was an integral domain, $R(y)$ would be one, too (as a localization of R[y]). Hence, $Frac(R(y))$ would be a field.
But I am not sure if $R \otimes_{k} L = R[y]$ is even an integral domain since the elements $y$ may have relations over $R$. So it is not clear if this is an isomorphism of fields or just rings.