Over a ring A let PA 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 ⊗A() 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 T-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.
