Timeline for Problems where we can't make a canonical choice, solved by looking at all choices at once
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| Dec 21, 2010 at 10:07 | comment | added | darij grinberg | I think a better point along these lines is this: When $A$ is a finite-dimensional (probably Artinian is enough) semisimple $k$-algebra, then $A$ decomposes into a direct sum of $A$-left modules. But these are not canonical (although, up to isomorphism, they are). Same for $A$-right modules. But if we switch to $\left(A,A\right)$-bimodules (which sort of are several $A$-left modules welded together and several $A$-right modules welded together), they become canonical (up to order). | |
| Dec 21, 2010 at 5:31 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |