On semiperfect associative pairs |
| |
| Authors: | Miguel Angel Fortes Escalona Inmaculada Delas Peñas Cabrera Esperanza Sánchez Campos |
| |
| Affiliation: | Departamento de álgebra, Geometría y Topologia , Universidad de Málaga , Apartado 59, Málaga, 29080, Spain E-mail: esperanz@agt.cie.uma.es |
| |
| 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. |
| |
| Keywords: | |
|
|
