Base change for Kähler differentials
= Base change for Kähler differentials
{title2=$\Omega_{(A\otimes_k k')/k'}=\Omega_{A/k}\otimes_k k'$}
The <Kähler differentials> commute with extension of the base ring. A derivation of the base-changed algebra that kills $k'$ is determined by its restriction to $A\otimes1$, and the <Leibniz rule> provides its unique extension. No flatness hypothesis is required for this isomorphism.