Timeline for Contramodule as direct limit of its finitely generated subcontramodules
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2021 at 14:26 | history | edited | Leonid Positselski | CC BY-SA 4.0 |
small formatting improvement
|
| Feb 18, 2021 at 12:22 | comment | added | Leonid Positselski | Now let us consider one of the simplest examples of an infinite-dimensional coalgebra: the coalgebra $C$ whose dual topological algebra $C^*$ is the algebra of formal power series in one variable, $C^*=k[[t]]$. Then all the nonzero subcontramodules of the $C$-contramodule $C^*$ are isomorphic (as $C$-contramodules) to $C^*$. Hence they are not finitely generated as objects of $C{-}\mathbf{contra}$. So the direct limit of finitely generated subcontramodules of $C^*$ is zero, which is different from $C^*$. | |
| Feb 18, 2021 at 12:14 | history | answered | Leonid Positselski | CC BY-SA 4.0 |