Hopfian module

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


  • 1 T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York (1999).
Title Hopfian module
Canonical name HopfianModule
Date of creation 2013-03-22 14:20:21
Last modified on 2013-03-22 14:20:21
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 9
Author CWoo (3771)
Entry type Definition
Classification msc 16D99
Related topic HopfianGroup
Defines cohopfian module