0
$\begingroup$

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?

Thanks!

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.