Timeline for Origin of the theorem on the existence of the smallest field of definition of an affine variety
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2012 at 1:32 | answer | added | user27056 | timeline score: 3 | |
| Oct 29, 2012 at 0:04 | answer | added | Jim Humphreys | timeline score: 5 | |
| Oct 28, 2012 at 23:57 | history | edited | Jim Humphreys |
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| Oct 28, 2012 at 21:57 | answer | added | Benjamin Dickman | timeline score: 5 | |
| Oct 28, 2012 at 21:51 | comment | added | Markus Schweighofer | I am sorry, I don't know the answer to your question but I just realized that you can prove it using Gröbner basis. Let $E$ and $F$ be subfields of $K$ such that $I$ is generated by polynomials with coefficients in $E$ and in $F$, respectively. Then choose reduced Gröbner bases $G$ and $H$ of $I$ with respect to the same term ordering having all coefficients in $E$ and in $F$, respectively. Now both $G$ and $H$ are reduced Gröbner bases of $I$ also over $K$. Because of the unicity of the reduced Gröbner basis, we have $G=H$. Hence $I$ is generated by polynomials with coefficients in $E\cap F$. | |
| Oct 28, 2012 at 21:00 | history | asked | Makoto Kato | CC BY-SA 3.0 |