  In 2008 N.~Q.~Chinh and P.~H.~Nam characterized principal ideal domains as
integral domains that satisfy the follo\-wing two conditions: (i) they are
unique factorization domains, and (ii) all maximal ideals in them are
principal. We improve their result by giving a characterization in which each
of these two conditions is weakened. At the same time we improve a theorem by
P.~M.~Cohn which characterizes principal ideal domains as atomic B\'ezout
domains. We will also show that every PC domain is AP and that the notion of PC
domains is incomparable with the notion of pre-Schreier domains (hence with the
notions of Schreier and GCD domains as well).
