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
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