Timeline for Tensor of Hom spaces over an algebra
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2018 at 12:44 | vote | accept | Jhon M. | ||
| May 16, 2018 at 8:30 | answer | added | user106723 | timeline score: 3 | |
| May 15, 2018 at 18:41 | comment | added | Mohan | As @abx comment says, if not injective, you can reduce to the case of finite dimensional case easily. For example, if $u$ as in the comment is not injective, you have $u(\sum \alpha_i\otimes \beta_i)=0$, a finite sum and each of the $\alpha_i,\beta_i$ involve only finitely many basis elements. | |
| May 15, 2018 at 16:36 | comment | added | abx | Put $M=k^{(I)}$ and $N=k^{(J)}$. What you are asking is whether the natural map $u:A^{I}\otimes _A A^{J}\rightarrow A^{I\times J}$ satisfying $u((x_i)\otimes (y_j))=(x_iy_j)$ is injective. I would guess this is true, but I don't see an argument right now. | |
| May 15, 2018 at 16:31 | review | Close votes | |||
| May 15, 2018 at 23:04 | |||||
| May 15, 2018 at 15:39 | review | First posts | |||
| May 15, 2018 at 15:46 | |||||
| May 15, 2018 at 15:38 | history | asked | Jhon M. | CC BY-SA 4.0 |