Timeline for Existence of prime ideals and Axiom of Choice.
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 2 at 2:32 | comment | added | Kapil | Note that the D. Scott reference is an abstract. | |
| Jun 2, 2012 at 23:46 | comment | added | godelian | @ Andreas: Nice! I didn't notice this direct deduction. @AliReza: Sorry, I wouldn't know how to answer your question since I'm not sure what exactly you have in mind or if I understand what exactly you mean. It all seems very subjective and relative. | |
| Jun 1, 2012 at 12:41 | comment | added | Ali Reza | Thank you very much for your references and sketch of proofs. But when I read your claims another Question came in my mind to. Is it true that the structure of maximal ideals are more algebraic than prime ideals? I mean that When I consider the prime ideals in commutative rings I could translate it to the language of boolean algebra and lattice theory, But maximal ideals are not wide enough to conduct it to another structure theory such as boolean algebra ...? | |
| Jun 1, 2012 at 12:28 | comment | added | Andreas Blass | The apparently stronger form, where $P$ includes $I$ and is disjoint from $S$, follows from the weaker form (mere existence of prime ideals) by applying the weaker form to the ring you get by localizing $R$ at $S$ (i.e., inverting all elements of $S$) and dividing by (the image of) $I$. | |
| Jun 1, 2012 at 12:23 | vote | accept | Ali Reza | ||
| Jun 1, 2012 at 10:06 | history | answered | godelian | CC BY-SA 3.0 |