Timeline for Characterizing the surcomplex numbers
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| May 3, 2011 at 16:44 | comment | added | James Propp | Thanks! I see that Norman Alling, in his book "Foundations of Analysis over Surreal Number Fields" (which I obtained after posting my query), proves that the surreal numbers are real-closed by identifying them with formal power series of a suitable kind. He does not (as far as I can tell) characterize ${\bf Cx}$ functorially. Perhaps the right functorial characterization would involve fields equipped with an involution (complex conjugation) that satisfies various properties and in particular induces partial orderings based on real part, imaginary part, and modulus. | |
| May 3, 2011 at 5:59 | comment | added | Qiaochu Yuan | The property that adjoining $i$ makes your field algebraically closed is called being real closed and has many, many equivalent formulations: en.wikipedia.org/wiki/Real_closed_field | |
| May 3, 2011 at 5:49 | history | asked | James Propp | CC BY-SA 3.0 |