Timeline for Rings satisfying the polynomial equation $x^4=x^2$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 2, 2015 at 23:33 | comment | added | M. Farrokhi D. G. | The only assumption on the rings $R$ is associativity, and finiteness if any counting method is applicable. | |
| Feb 2, 2015 at 23:29 | vote | accept | M. Farrokhi D. G. | ||
| Feb 2, 2015 at 20:05 | comment | added | Terry Tao | Taking differences three times ($(x+1)^4-x^4 = (x+1)^2-x^2$, etc.) gives $24x=0$ for all $x$. EDIT: Actually, just taking $x=2$ gives the stronger claim $12=0$. | |
| Feb 2, 2015 at 19:09 | comment | added | zeb | It isn't too hard to show that $2xy = 2yx$ for any $x,y$ in such a ring (it follows quickly from $2x^3 = 2x$). | |
| Feb 2, 2015 at 18:22 | comment | added | YCor | I know people for which every ring is associative, unital, and commutative. I know people for which every ring is associative and unital, but not necessarily commutative. I know people for which rings are not assumed with any of these properties. In each of these communities, some people are convinced that their conventions are universal. Nevertheless I think it is useful to spare the reader from guessing which convention they use, it's really not a big effort. | |
| Feb 2, 2015 at 15:20 | comment | added | Qfwfq | @YCor: usually rings are assumed to be associative and unital, but not necessarily commutative. I would assume the OP has that definition in mind.. | |
| Feb 2, 2015 at 14:10 | answer | added | Zurab Silagadze | timeline score: 14 | |
| Feb 2, 2015 at 13:59 | comment | added | YCor | Do you assume rings to be associative? unital? | |
| Feb 2, 2015 at 10:51 | history | asked | M. Farrokhi D. G. | CC BY-SA 3.0 |