Z, Q, R, C are all domains.

It is sufficient to note that C is a domain, since then a forteriori all of its subrings are domains.

The ring Z/nZ is a domain if and only if n is a prime.

The polynomial ring R[X] is a domain if and only if R is a domain. For a proof, see the next page.

If R is a field, then f is an irreducible polynomial in R[X] if and only if R[X]/(f) is a domain.

The Gaussian integers Z+Zi is a domain.

(It is a subring of the domain C.)