Timeline for The difference between vector space and group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2014 at 4:58 | comment | added | Alex Youcis | It might be worth mentioning, if it is non-obvious, that there are (many!!) groups which cannot be given the structure of a vector space. For example, $\mathbb{Z}$, or $\mathbb{Z}/(6)$. | |
| Jul 27, 2014 at 4:57 | comment | added | 89085731 | @BrianFitzpatrick That's what I need. I just wondering if I can define a basis in the $\mathbb{Z}$ module. For example let $x^2=x\cdot x$,$x^{-1}$ as the inverse element of $x$，$x^{-2}=x^{-1}\cdot x^{-1}$ | |
| Jul 27, 2014 at 4:37 | comment | added | Brian Fitzpatrick | Not directly related to your listed questions, but you might find interesting the definition of an $R$-module where $R$ is a ring. A vector-space over a field $k$ is the same thing as a $k$-module while an abelian group is the same thing as a $\Bbb Z$-module. | |
| Jul 27, 2014 at 3:24 | answer | added | Hubble | timeline score: 18 | |
| Jul 27, 2014 at 3:10 | answer | added | user_of_math | timeline score: 1 | |
| Jul 27, 2014 at 2:54 | history | asked | 89085731 | CC BY-SA 3.0 |