Endomorphism rings of finitely generated projective modules

Abstract

Over a ring A let P A be a finitely generated projective right A-module with A-endomorphism ring B. Anderson has called PA an injector, perfect injector, projector, perfect projector, if the functor F = BP 0A ( ) preserves injectives, injective hulls, projectives, projective covers, respectively. Call PA a flatjector if F preserves flat modules. Injectors, flatjectors, and projectors are characterized. The radical of a module over B is studied, and necessary and sufficient conditions are given for the radical of B to be left !F-nilpotent. Perfect injectors are characterized. Previous characterizations of perfect projectors have assummed the ring A to be left perfect. Here characterizations are obtained using substantially weaker conditions on PA