Right self-injective rings whose essential right ideals are two-sided.

A ring R of the kind described by the title is called a right g-ring and is characterized by the property that each of its right ideals is quasi-injective as a right i?-module. The principal results of this paper are Theorem 6, which describes how an arbitrary right g-ring is constructed from division rings, local rings, and right #-rings with no primitive idempotent, and Theorem 5 which shows that a right g-ring cannot have an infinite set of orthogonal noncentral idempotents.