Timeline for If $M_n(R)$ and $M_m(R)$ satisfy the same polynomial identities is it true that $m=n$?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| May 14, 2013 at 21:36 | comment | added | Thiago | @Pasha, thank you very much for the references. They will be very useful! | |
| May 13, 2013 at 9:00 | history | edited | Pasha Zusmanovich | CC BY-SA 3.0 |
added 942 characters in body
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| May 13, 2013 at 5:08 | comment | added | Mariano Suárez-Álvarez | @Thiago, I was just providing an example to Pasha's second paragraph, quite independently of what the question asked for. | |
| May 13, 2013 at 0:56 | comment | added | Thiago | Mariano, also in this case, $R$ is not PI. | |
| May 13, 2013 at 0:53 | comment | added | Thiago | Right, Misha! I assume R to be an associative ring. In particular, Pasha, the free associative algebra of rank >1 is not PI, as well. I will fix this. Thanks for the answers. | |
| May 12, 2013 at 23:26 | comment | added | Misha | Thiago has the assumption that $R$ satisfies a nontrivial polynomial identity. Associativity is, of course, an identity, but, I suspect, he just forgot to assume that $R$ is an associative ring. | |
| May 11, 2013 at 10:00 | comment | added | Mariano Suárez-Álvarez | If $R$ is a ring of row-finite column finite infinite matrices, then $R\cong M_2(R)$. | |
| May 11, 2013 at 9:17 | history | answered | Pasha Zusmanovich | CC BY-SA 3.0 |