Give an example of infinite integral domain that has characteristic 3.
I know the result which states that finite integral domain has characteristic either 0 or prime.We have example of infinite integral domain that is $\Bbb Z$ but it has characteristic $0$.I am stuck here how to form an example of infinite integral domain with characteristic 3?
You can consider the ring $R = \mathbb{F}_3[x]$ of univariate polynomials over the finite field of $3$ elements. As $\mathbb{F}_3$ is a field, thus an integral domain, $R$ will be an integral domain too, and it will have characteristic $3$. Clearly, $R$ is infinite.