I have studied the following theorem:

Let ${}_{R}Q_S$ a faithfully balanced bimodule. Then ${}_{R}Q$ is a generator if and only if $Q_{S}$ is finitely generated and projective.

Can I say the same reversing left and right? So is it true that $Q_S$ is finitely generated and projective if and only if ${}_{R}Q$ is a generator? I think yes, but I'd like to be sure! Then I could say that ${}_{R}Q$ is a progenerator if and only if $Q_S$ is?



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