Commutative perfect 𝑄𝐹-1 rings

Abstract

If R is a commutative artinian ring, then it is known that every finitely generated faithful R-module is balanced (i.e. has the double centralizer property) if and only if R is a quasi-Frobenius ring. In this note, constructing new nonbalanced modules we prove that the assumption on R to be artinian can be replaced by the weaker condition that R is perfect.