# Infinite Field With Characteristic 5?

• Mar 18th 2010, 09:19 AM
mathematicalbagpiper
Infinite Field With Characteristic 5?
One of my study guide questions says to give an example of such a field. I'm sure there's more than one example. From there, how would I show it has said characteristic?
• Mar 18th 2010, 10:10 AM
Black
$\mathbb{Z}_5(x)=\{f(x)/g(x)|\, f(x),g(x) \in \mathbb{Z}_5[x], \, g(x) \not= 0\}$ is one, since unity 1 has order 5 under addition.