Timeline for Terminology: Algebras where long strings of products are 0?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Nov 1, 2010 at 21:49 | comment | added | Greg Marks | (I guess jsMath gets rendered in the comments sections, but HTML markup doesn't. Weird.) | |
| Nov 1, 2010 at 21:43 | comment | added | Greg Marks | ... Restricted Burside Problem in his 1992 monograph <i>Nil Rings and Periodic Groups</i>. Sample result: C. Procesi's theorem that a periodic group contained in the unit group of a polynomial identity algebra must be locally finite. | |
| Nov 1, 2010 at 21:40 | comment | added | Greg Marks | I'm happy to hear this was of some small help. My apologies for the lengthy delay in replying to your message. I'm not sure how persuasive a justification you'll find this, but local nilpotence of algebras is connected with the Burnside Problem for groups, asking whether a finitely generated periodic group need be finite. The first counterexample was an immediate consequence of E. S. Golod's example of a finitely generated nil but not nilpotent algebra (thus in between nil and locally nilpotent). E. Zelmanov discusses local nilpotence of algebras in the context of his solution to the ... | |
| Jun 30, 2010 at 23:59 | comment | added | Dylan Thurston | Thanks for the comments! I hadn't thought about that distinction. Local nilpotence seems like a rather odd condition; I don't yet see where it would be useful. | |
| Jun 30, 2010 at 5:23 | history | answered | Greg Marks | CC BY-SA 2.5 |