Maximal and minimal ideals of centrally essential rings

We show that a ring $R$ with center $Z(R)$ such that the module $R_{Z(R)}$ is an essential extension of the module $Z(R)_{Z(R)}$ need not be right quasi-invariant, i.e., not all maximal right ideals of the ring $R$ are ideals. In terms of the central essentiality property, we obtain sufficient conditions for the fact that all maximal right ideals are ideals.