Timeline for Hom(A,C) ⊗ Hom(B,D) injects into Hom(A⊗B,C⊗D): when? why?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21 at 20:40 | comment | added | Smiley1000 | Could someone explain how we obtain $\sum\lambda(f_i(a))g_i=0$? | |
| Aug 5, 2011 at 18:58 | comment | added | Martin Brandenburg | There is a general criterion when an element in a tensor product of modules $M \otimes N$ is zero: Let $E$ be a generating set of $M$ and $F$ be a generating set of $N$, then a typical element of $M \otimes N$ has the form $\sum_{e \in E} e \otimes n_e$. It vanishes if and only if there is a matrix $(\lambda_{e,f})_{e,f}$ over $R$, whose support is finite, such that $n_e = \sum_{f \in F} \lambda_{e,f} f$ for all $e$ and $0 = \sum_{e \in E} \lambda_{e,f} e$ for all $f$. | |
| Aug 3, 2011 at 18:21 | comment | added | Anton Geraschenko | I think this is the only trick I know for proving that something in a tensor product is zero. Fortunately, it always works. | |
| Aug 3, 2011 at 18:18 | vote | accept | darij grinberg | ||
| Aug 3, 2011 at 18:18 | comment | added | darij grinberg | Wonderful proof! | |
| Aug 3, 2011 at 18:10 | history | answered | user2035 | CC BY-SA 3.0 |