faithful module

Let $R$ be a ring, and let $M$ be an $R$-module. We say that $M$ is a faithful $R$-module if its annihilator ${\mathrm{ann}}_R(M)$ is the zero ideal.

We say that $M$ is a fully faithful $R$-module if every nonzero $R$-submodule of $M$ is faithful.

Title	faithful module
Canonical name	FaithfulModule
Date of creation	2013-03-22 12:01:35
Last modified on	2013-03-22 12:01:35
Owner	antizeus (11)
Last modified by	antizeus (11)
Numerical id	7
Author	antizeus (11)
Entry type	Definition
Classification	msc 16D80
Synonym	fully faithful module