I was trying to prove the following statement.
Let $f:A\to B $ be a ring homomorphism. $M$ is a finitely generated $A$-module. Then show that $V(\mathrm{Ann}_A(M)^e)=V(\mathrm{Ann}_B(B\otimes_A M))$.
My attempt: A simple observation says that, $Ann(M))^e \subseteq Ann(B \otimes_A M)$. Hence,$V(Ann(B\otimes_A M)\subseteq V((AnnM)^e))$ I was unable to do the converse part.