Give an example of an integral domain which has an infinite number of element yet its finite characteristics

Question

Give an example of an integral domain which has an infinite number of element yet its finite characteristics?

I thinks $\mathbb{Q}$

Is it correct ??

Answer 1

Take $F := \mathbb{F}_p(x)$, the field of rational functions in one variable over the prime field $\mathbb{F}_p$.

Answer 2

X is a set of infinity elements . Then P(x) is also infinity . And P(x) with respect to symmetric difference & intersection forms a infinite integral domain with Cher 2