Characterisation of two-sided PF-rings (Q1177266)

A ring \(R\) is called a two-sided \(PF\)-ring (or a ring with perfect duality) if both \(_ RR\) and \(R_ R\) are injective cogenerators, i.e. \(R\) is a left and right \(PF\)-ring. The following characterisation of such rings is obtained. Theorem. A ring \(R\) is a two sided \(PF\)-ring iff the modules \(_ RR\) and \(R_ R\) are both finitely cogenerated and linearly compact and the duals of simple modules are also simple.