$A$ is noetherian.
When taking quotient of $A$, is there something like taking localization:
$\operatorname{Ass}_{S^{-1}A}(S^{-1}M)=\operatorname{Spec}(S^{-1}A)\cap \operatorname{Ass}_A(M)$
I’m studying primary decomposition. In this circumstance it’s natural to take quotient rather than localization. Although taking quotient lose some information, I still wonder if there is any useful connection between $\operatorname{Ass}_A(M)$ and $\operatorname{Ass}_{A/α}(A/α\otimes_AM)$?