  In this paper we prove that if $R$ is a commutative, reduced, local ring,
then $R$ is Hopfian if and only if the ring $R[x]$ is Hopfian. This answers a
question of Varadarajan, in the case when $R$ is a reduced local ring. We
provide examples of non-Noetherian Hopfian commutative domains by proving that
the finite dimensional domains are Hopfian. Also, we derive some general
results related to Hopfian rings.
