Timeline for Can the trivial module be stably free for a monoid ring?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2016 at 20:09 | vote | accept | Benjamin Steinberg | ||
| Aug 26, 2016 at 19:16 | answer | added | Pace Nielsen | timeline score: 4 | |
| Aug 26, 2016 at 16:30 | comment | added | Pace Nielsen | The case $P_{\infty}$ should be the direct limit of the finite cases, which are dealt with in Cohn's paper. See doi:10.1016/0040-9383(66)90006-1 and in particular, Theorem 2.3 and Theorem 6.1 (in connection with the material from Lam's book, if necessary). | |
| Aug 26, 2016 at 14:57 | comment | added | Benjamin Steinberg | @PaceNielsen, Thanks! I'll have to get a hold of Lam. This gives me hope the more general question might work. But what happens if I take $P_{\infty}$ meaning I take countably infinitely many unilateral shifts xx*=1 with orthogonal x*x's. Does it still have IBN? | |
| Aug 26, 2016 at 14:46 | comment | added | Pace Nielsen | The contracted monoid ring of $P_2$ doesn't have the rank condition, but it actually does have the IBN property. See Lam's "Lectures on Modules and Rings" page 11, and exercise 1.5, for a discussion of this example and proof (originally due to Cohn). I'll think about your general questions some more. | |
| Aug 26, 2016 at 13:53 | history | edited | Benjamin Steinberg | CC BY-SA 3.0 |
added 185 characters in body
|
| Aug 26, 2016 at 13:38 | history | edited | Benjamin Steinberg | CC BY-SA 3.0 |
edited body
|
| Aug 26, 2016 at 13:32 | history | asked | Benjamin Steinberg | CC BY-SA 3.0 |