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Preliminaries.- Semi-perfect rings.- Morita duality.- Left QF-3 rings.- The structure of QF-3 rings.- Are noetherian, left QF-3 rings artinian, so QF-3?.- Dominant dimension.- Conjectures arising from Nakayama's conjecture.- QF-3 rings and rings of finite representation type.- The double centralizer condition.- QF-13 rings.- QF-3 rings and categories of projective modules.