Timeline for An elementary question about the Krull dimension of modules
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2010 at 7:45 | vote | accept | TmobiusX | ||
| Aug 4, 2010 at 1:50 | comment | added | TmobiusX | Does the equality hold when M is not finite? | |
| Aug 3, 2010 at 9:25 | comment | added | Angelo | To the OP: I think this should be proved in any book that discusses dimensions of modules. In case as Martin says it is a very easy exercise. To Dylan: the dimension of the spectrum of a ring A is the Krull dimension of A, and the definition for modules is a useful generalization. It can also be interpreted as the Krull dimension of the ring modulo the annihilator of the module (I am always referring to finite modules over noetherian rings). | |
| Aug 3, 2010 at 8:45 | comment | added | Martin Brandenburg | $dim(X \cup Y) = max(dim(X),dim(Y))$ is a an easy exercise in general topology. | |
| Aug 3, 2010 at 8:04 | comment | added | TmobiusX | Is there a reference for this result? Thanks! | |
| Aug 3, 2010 at 7:50 | comment | added | Dylan Wilson | Thanks! Is it called the "Krull dimension" though? That's what confused me... | |
| Aug 3, 2010 at 7:35 | history | answered | Angelo | CC BY-SA 2.5 |