# 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 ${\rm ann}_{R}(M)$ 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 FaithfulModule 2013-03-22 12:01:35 2013-03-22 12:01:35 antizeus (11) antizeus (11) 7 antizeus (11) Definition msc 16D80 fully faithful module