Timeline for Quotient of $Z[x_1,...,x_n]$ by a maximal ideal is a finite field
Current License: CC BY-SA 3.0
4 events
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| Oct 11, 2013 at 4:19 | comment | added | Steven Landsburg | @BenjaminSteinberg: Though if your point was that it takes additional argument to conclude that $k$ is finite, that's of course correct. | |
| Oct 11, 2013 at 4:18 | comment | added | Steven Landsburg | @BenjaminSteinberg: Yes, there are two parts to the argument --- first, $k$ is finitely generated over the prime field, then this implies that $k$ is finite. Wikipedia uses the phrase "generalized Nullstellensatz" to mean the conjunction of these two statements; I'm not sure how standard that is. | |
| Oct 11, 2013 at 2:43 | comment | added | Benjamin Steinberg | Actually the fact that the image of Z is finite just means that k is finitely generated over the prime field. But according to the Wikipedia article it is part of the generalized Nullstellensatz that k is a finite extension of Z/p. | |
| Oct 11, 2013 at 0:30 | history | answered | Steven Landsburg | CC BY-SA 3.0 |