Let $R$ be a ring with unity (not necessarily commutative). Let ${}_R Mod$ be the category of left $R$modules. If ${}_R Mod$ has a projective generator with commutative endomorphism ring , then does ${}_R Mod$ have a finitely generated projective generator with commutative endomorphism ring ?
$\begingroup$
$\endgroup$
2

$\begingroup$ I still don’t know the answer, but I raised exactly the same question in a comment on this MSE question some time ago: math.stackexchange.com/questions/1364337/…. It would be interesting to know whether your interest in the question is for similar reasons. $\endgroup$– Jeremy RickardJan 1, 2019 at 10:17

$\begingroup$ @JeremyRickard: I just saw your comment in the linked question ... and yes I was also thinking about how to distinguish the category of modules over a commutative ring from that over a general ring .. $\endgroup$– user521337Jan 2, 2019 at 5:55
Add a comment
