Timeline for Freeness of a Z[x]-module
Current License: CC BY-SA 3.0
3 events
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| Jul 13, 2014 at 16:41 | comment | added | Thomas | Another way to see this is to show that the map $R\to R'$ with $f\mapsto f_{\mid \mathbb N}$ is $1-1$, since any $f\in R$ that is zero at infinitely many values is zero everywhere. So, cardinality-wise, $R'$ must be at least as big as $R$. | |
| Jul 13, 2014 at 16:01 | comment | added | Thomas | Really? $R'$ contains uncountably many elements, I think. Maybe I'm mistaken, but it seems obvious that if you have any sequence of integers, the function: $$f(x)=\sum_{n\in\mathbb N} a_n(x)_n$$ is defined for all natural numbers, satisfies the property since $f$ is locally integer polynomial, and each different sequence gives a different memeber of $R'$. Maybe you mean $R'\cap \mathbb Q[x]$? ($(x)_n$ being the falling factorial.) | |
| Mar 12, 2014 at 6:12 | history | answered | joaopa | CC BY-SA 3.0 |