Morita dualities associated with the R-dual functors

Abstract

We study the dualities induced by a ring R such that every finitely generated submodule of E( R R) is torsionless (left QF-3″ rings) and use them to obtain new information about these rings. The left-right symmetry of this condition is characterized in terms of a linear compactness property, and we use this fact to study QF-3″ rings with certain chain conditions. In particular, we show that a QF-3″ maximal quotient ring with ACC or DCC on essential left ideals is left artinian and QF-3.