Timeline for Other Ring Structures on $\mathbb{Q}$
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2011 at 21:55 | vote | accept | Aeryk | ||
| Aug 31, 2011 at 19:07 | answer | added | Noah Stein | timeline score: 2 | |
| Aug 31, 2011 at 19:00 | answer | added | Amit Kumar Gupta | timeline score: 13 | |
| Aug 31, 2011 at 18:38 | answer | added | Pace Nielsen | timeline score: 2 | |
| Aug 31, 2011 at 18:26 | answer | added | Neil Strickland | timeline score: 3 | |
| Aug 31, 2011 at 15:50 | comment | added | Joel David Hamkins | If you are only slightly generous with the notion of formula, you will pick up all countably infinite computable rings, since the formulas will allow you to specify any computable function. For example, Julia Robinson proved that the integers are definable inside the rational field in a primitive manner, and then any computable function y=f(x) is specified by there being an integer solution to a certain diophantine equation involving x and y and other integer variables. So the answer to the question will depend greatly on the details of what kind of definition you allow. | |
| Aug 31, 2011 at 15:18 | answer | added | Gerhard Paseman | timeline score: 0 | |
| Aug 31, 2011 at 14:55 | comment | added | Aeryk | I wasn't thinking rational functions because I feel like other properties arising from multiplication and addition should be allowed, such as prime factors, gcd, partitions, etc. I'll edit the original post to reflect this. | |
| Aug 31, 2011 at 14:52 | history | edited | Aeryk | CC BY-SA 3.0 |
added 87 characters in body; added 12 characters in body
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| Aug 31, 2011 at 14:52 | answer | added | Ben McKay | timeline score: 2 | |
| Aug 31, 2011 at 14:51 | comment | added | darij grinberg | Maybe you want "closed formulas" to mean something like "the operations are rational functions"? | |
| Aug 31, 2011 at 14:50 | comment | added | darij grinberg | Read "and" for "or" in my comment above. | |
| Aug 31, 2011 at 14:50 | comment | added | darij grinberg | What about taking some permutation of $\mathbb Q$ which fixes $0$ or $1$ (if you want this new ring to have the same $0$ and $1$ as the original ring $\mathbb Q$; if not, then you don't have to require even this) and conjugating the operations $+$ and $\times$ by this permutation? | |
| Aug 31, 2011 at 14:44 | history | asked | Aeryk | CC BY-SA 3.0 |