Polynomial rings over commutative reduced Hopfian local rings

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 [ 16 ], 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.