Vol. 47, No. 1, 1973

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Endomorphism rings of finitely generated projective modules

Robert Wilmer Miller

Vol. 47 (1973), No. 1, 199–220

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.

Mathematical Subject Classification
Primary: 16A50
Received: 7 January 1972
Published: 1 July 1973
Robert Wilmer Miller