Let $A$ be a Noetherian ring and $\mathfrak a$ be an ideal of $A$. Then it is well-known that the associated prime ideas of $\mathfrak a$ are those prime ideals that have the form $(\mathfrak a:x)$ for $x \in A$.
I want to know whether Noetherian condition is necessary or not, that is, for an arbitrary ring $A$ (always commutative with $1$) knowing that an ideal $\mathfrak a$ of $A$ has a minimal primary decomposition, is it possible to obtain the same result?