On Hopfian Rings

Varadarajan, K.

Department of Mathematics and Statistics University of Calgary Calgary, Alberta Canada. T2N 1N4 E-mail: [email protected]

Acta Mathematica Hungarica 83(2):p 17-26, April 1999.

The main results proved in this paper are:(i) If R is a boolean hopfian ring then the polynomial ring R[T] is hopfian.(ii) Let R and S be hopfian rings. Suppose the only central idempotents in S are 0 and 1 and that S is not a homomorphic image of R. Then R × S is a hopfian ring.