Given a ringR, consider the condition: (*) every maximal right ideal ofRcontains a maximal ideal ofR. We show that, for a ringRand 0 ≠e2=e∈Rsuch thatele⫋eReevery proper idealIofRRsatisfies (*) if and only if eRe satisfies (*). Hence with the help of some other results, (*) is a Morita invariant property. For a simple ringRR[x] satisfies (*) if and only ifR[x] is not right primitive. By this result, ifRis a division ring andR[x] satisfies (*), then the Jacobson conjecture holds. We also show that for a finite centralizing extensionSof a ringRRsatisfies (*) if and only ifSsatisfies (*).