Example of infinite field of characteristic $p\neq 0$ Can you give me an example of infinite field of characteristic $p\neq0$?
Thanks.

Another construction, using a tool from the formal logic: the ultraproduct.
The cartesian product of fields
$$P = {\Bbb F}_p\times{\Bbb F}_{p^2}\times{\Bbb F}_{p^3}\times\cdots$$
isn't a field ("isn't a model of..." ) because has zero divisors:
$$(0,1,0,1,\cdots)(1,0,1,0\cdots)=(0,0,0,0,\cdots).$$
The solution is taking a quotient: let $\mathcal U$ be a nonprincipal ultrafilter on $\Bbb N$. Define
$$(a_1,a_2,\cdots)\sim(b_1,b_2,\cdots)$$
when
$$\{n\in\Bbb N\,\vert\, a_n=b_n\}\in\mathcal U.$$
The quotient $F=P/\sim$ will be a infinite field of characteristic $p$.
