Timeline for What is the theory of local rings and local ring homomorphisms?
Current License: CC BY-SA 3.0
6 events
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| Feb 28, 2012 at 23:25 | comment | added | Zhen Lin | I'm not sure your definition of $\mathfrak{m}$ is geometric/coherent. Certainly, $\exists z . \; z - x y z = 1$ is a coherent formula, but the problem is that what we want is $(\forall y. \; \exists z . \; z - x y z = 1) \vdash x \in \mathfrak{m}$, and this is not a coherent sequent. | |
| Feb 28, 2012 at 10:36 | comment | added | Martin Brandenburg | You are right. I just wanted to mention that with this axiomatization, 1+2 are fulfilled, but 3 is not. Zhen already asked specifically about the equation $R = R^* \cup \mathfrak{m}_R$ (in logical language), therefore I've added this not just as a comment. I hope it's ok ... | |
| Feb 28, 2012 at 10:28 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
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| Feb 28, 2012 at 10:23 | comment | added | Zoran Skoda | Martin, this is a useful comment, but not an answer to his question: is it possible to axiomatize the theory of local rings as a coherent theory or at least a geometric theory in the technical sense of the word. | |
| Feb 28, 2012 at 10:07 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
added 351 characters in body; added 3 characters in body
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| Feb 28, 2012 at 10:00 | history | answered | Martin Brandenburg | CC BY-SA 3.0 |