# Does there exist an infinite field with characteristic $p$ for any prime $p$ that is not too big? [duplicate]

Does there exist an infinite field with characteristic $p$ for any prime $p$?

I haven't seen any such fields in my course yet.

take the field of fractions of polynomials in $F_p[x]$, i.e. the set of elements
$P(x)/Q(x)$
where $P$, $Q \in F_p[x]$ (and $Q \ne 0$).