# Hopfian module

A left (right) module $M$ over a ring $R$ is Hopfian if every surjective $R$-endomorphism of $M$ is an automorphism. Dually, a left (right) $R$-module $M$ is cohopfian if every injective $R$-endomorphism of $M$ is an automorphism.

## References

• 1 T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York (1999).
Title Hopfian module HopfianModule 2013-03-22 14:20:21 2013-03-22 14:20:21 CWoo (3771) CWoo (3771) 9 CWoo (3771) Definition msc 16D99 HopfianGroup cohopfian module