Is there a homological criterion for the condition $A(B \cap C) = AB \cap AC$ for ideals in a ring $R$? By "homological" I mean a statement such as "the given equation holds if and only if (some Tor, Ext, local cohomology, etc) group vanishes/does not vanish".
Note that this is a local question, since we are asking when the inclusion $A(B \cap C) \to AB \cap AC$ is surjective.
Note also that this equation always holds in a Dedekind domain.
This is inspired by the fact that $AB = A \cap B$ if and only if $Tor^1(R/A,R/B) = 0$.
