Timeline for Is there any monoid in which the product of two non-invertible elements could be invertible?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 19, 2013 at 19:08 | vote | accept | Amir Asghari | ||
| Sep 17, 2013 at 18:00 | comment | added | Amir Asghari | @StefanKohl At the first glance, I didn't get the point of Todd's answer. But, then I worked on the details, and I got it. Yet, I thank you for the details you added | |
| Sep 17, 2013 at 16:02 | comment | added | Stefan Kohl♦ | @AmirAsghari: In Todd's example, $A(e_1) = A(e_2) = e_1$, thus $A$ is not invertible. Further, $e_1 \notin {\rm im}(B)$, thus $B$ is not invertible either. | |
| Sep 17, 2013 at 15:43 | comment | added | Todd Trimble | Heck, why even bother with vector spaces. For monoids, just use the same idea applied to the set $\mathbb{N}$. But since this came up while discussing linear algebra... | |
| Sep 17, 2013 at 15:42 | history | answered | Todd Trimble | CC BY-SA 3.0 |