Timeline for Different ways of having infinite global dimension

8 events

when toggle format	what		by	license	comment
May 22, 2015 at 12:58	comment	added	Fernando Muro		Thanks for your comments. I also think this is maybe a difficult question. Strange examples are... strange.
May 22, 2015 at 12:22	comment	added	Benjamin Steinberg		I think you can find such examples by googling but from what I read it is unknown if there is a ring which is both left and right noetherian whose simple modules all have finite projective dimension but who has infinite global dimension
May 22, 2015 at 11:36	history	edited	Benjamin Steinberg	CC BY-SA 3.0	added 211 characters in body
May 22, 2015 at 11:32	comment	added	Benjamin Steinberg		Let me think. But in any event this shows that if your hypothesis is true then all cyclic modules have finite projective dimension and your direct sum condition doesn't help. So what you really want is an example where each cyclic module has finite projective dimension which is unbounded.
May 22, 2015 at 10:47	comment	added	Fernando Muro		Sorry, your argument convinced me at a first glance, but I don't see the contradiction. There might be a sequence of cyclic modules with finite but divergent projective dimension.
May 21, 2015 at 18:14	history	edited	Benjamin Steinberg	CC BY-SA 3.0	added 274 characters in body
May 21, 2015 at 18:08	vote	accept	Fernando Muro
May 22, 2015 at 10:46
May 21, 2015 at 18:07	history	answered	Benjamin Steinberg	CC BY-SA 3.0