Timeline for When can we prove constructively that a ring with unity has a maximal ideal?
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3 events
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| Nov 28, 2009 at 17:45 | comment | added | Georges Elencwajg | Evaluation at a point of X is a character, independantly of X being Stein or not, so I know that O(X) does have a character. I have no idea of what would happen to Stein theory if the fundamental theorem of algebra didn't hold, nor to be frank to the rest of mathematics. | |
| Nov 28, 2009 at 17:03 | comment | added | Greg Kuperberg | You have to be careful about the basic structure of the complex numbers without countable choice. A Cauchy sequence may or may not be constructively Cauchy, and I read that the fundamental theorem of algebra only holds for polynomials whose coefficients are constructively Cauchy numbers. Possibly different definitions of Stein become inequivalent; and how do you know that O(X) even has a character? | |
| Nov 28, 2009 at 15:30 | history | answered | Georges Elencwajg | CC BY-SA 2.5 |