Abstract
A ring [Formula: see text] is called a left [Formula: see text]-ring if its left socle, [Formula: see text], is projective. Equivalently, [Formula: see text] is left [Formula: see text]-ring if the right annihilator of every maximal left ideal is of the form [Formula: see text], where [Formula: see text] is an idempotent in [Formula: see text]. In this paper, we characterize when a (trivial) Morita context or a generalized triangular matrix ring is a left [Formula: see text]-ring. Examples to illustrate and delimit the theory are provided.
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