Timeline for Question about an exact sequence
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2013 at 0:48 | vote | accept | Rolf Schwarz | ||
| Dec 16, 2012 at 12:38 | comment | added | Leonid Positselski | Actually, I've made a mistake: the converse statement is true. A left $A$-module $M$ is a generator of the abelian category of left $A$-modules if and only if the left $A$-module $A$ is a direct summand of a direct sum of copies of $M$. Indeed, $M$ being a generator means that there is a surjective $A$-module map onto any $A$-module $Q$ from a direct sum of copies of $M$. When the $A$-module $Q$ is projective, it follows that $Q$ is a direct summand of a direct sum of copies of $M$. | |
| Dec 16, 2012 at 3:12 | comment | added | Mariano Suárez-Álvarez | I always read «provided» as «only if» and get immediately confused :( | |
| Dec 16, 2012 at 0:35 | history | answered | Leonid Positselski | CC BY-SA 3.0 |