Math Help - Ideals of Integral Domains

1. Ideals of Integral Domains

Let D be an integral domain which is not a field. Show that {0} is a prime, but not a maximal, ideal of D.

2. Originally Posted by Coda202

Let D be an integral domain which is not a field. Show that {0} is a prime, but not a maximal, ideal of D.
{0} being prime is just the definition of an integral domain. if {0} was a maximal ideal, then D would be a domain with no non-zero proper ideal and hence it'd be a field.