Timeline for References discussing the category of ordered commutative rings
Current License: CC BY-SA 4.0
4 events
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| Feb 14, 2022 at 1:12 | comment | added | Alec Rhea | @PaulTaylor I refereed a paper on partially ordered commutative rings a few years back (it actually offered a categorical characterization of when a partially ordered ring is Archimedean if I remember correctly) and when I was writing this they occurred to me as the 'more categorical' choice, but they're pretty different beasts as far as how (my at least) intuition says they behave. That being said, I would be interested to read more about the category of partially ordered commutative rings as well if there are any references available. | |
| Feb 13, 2022 at 21:02 | comment | added | Paul Taylor | A person with good (ie categorical) taste would allow the order relation to be partial. The category of Archimedean ordered fields is just the complete lattice of subfields of $\mathbb R$. I doubt whether much interesting happens from a categorical point of view if you drop reciprocals or the Archimedean property but keep the total order. Maybe more interesting if you drop commutativity. Anyway, it's worth an open-minded but brief investigation. | |
| Feb 13, 2022 at 20:52 | history | edited | Alec Rhea | CC BY-SA 4.0 |
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| Feb 13, 2022 at 20:44 | history | asked | Alec Rhea | CC BY-SA 4.0 |