Modules over strongly semiprime rings

For a ring $A$, the following conditions are equivalent. 1) $A$ is a right strongly semiprime ring. 2) Every right $A$-module which is injective with respect to some essential right ideal of the ring $A$, is an injective module. 3) Every quasi-injective right $A$-module which is injective with respect to some essential right ideal of the ring $A$ is an injective module.