faithful module
FaithfulModule
2001-11-24 00:14:05
2003-09-20 21:34:54
Definition
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Let $R$ be a ring, and let $M$ be an $R$-module.
We say that $M$ is a {\it faithful} $R$-module
if its annihilator ${\rm ann}_R(M)$ is the zero ideal.
We say that $M$ is a {\it fully faithful} $R$-module
if every nonzero $R$-submodule of $M$ is faithful.