This is an exercise I found in a class test and I was struck trying to solve it.
Let $D$ be a Prüfer domain (*) and let be $\mathfrak{q}_1,\mathfrak{q}_2$ two primary ideals of $D$. Then prove that $\mathfrak{q}_1,\mathfrak{q}_2$ are coprime or one contains the other.
I tried using the fact that every localization of a Prüfer domain is a valuation domain, but it doesn't seem to solve.
Could someone give me a hint for the solution?
(*) A Prüfer domain, for what I know, is an integral domain in which every finitely generated non-zero ideal is invertible. The only characterization result I know is the one regarding valuation rings.
If $q_1,q_2$ are not coprime then they are contained in a maximal ideal, say $m$. In $R_m$ (which is a valuation ring) we then have $q_1R_m\subset q_2R_m$ or conversely, and you are done.