Abstract
It is known [8] that a semiperfect ring is characterized by the existence of a frame, i.e, a complete set of local orthogonal idempotents. We prove in this paper that a similar behaviour occurs when dealing with an associative pair A, namelyAis semiperfect if and only if Acontains a frame and Ā=A/Rad Ais unital. Moreover, we show that, when Ā is unital, the existence of a frame for Ais equivalent to the condition that every irreducible right A-module is isomorphic to e A/e(RadA) for some idempotent e of A.
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