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If R is a commutative artinian ring, then it is known that every faithful /J-module is balanced (i.e. has the double centralizer property) if and only if R is a quasi-Frobenius ring. In this note it is shown that the assumption on R to be artinian can be replaced by the weaker condition that R is noetherian.doi:10.2307/2039507 fatcat:4nrxgzjj4zgcvnlazxk7nt7l6u