[[Module theory MOC]]
# Faithful module

 A (left) $R$-[[module]] $V$ is said to be (left) **faithful** iff the [[Annihilator]] $\lAnn RS = 0$ is trivial, #m/def/module i.e. for any $r \in R$
 $$
\begin{align*}
r \odot  V = 0 \iff r = 0.
\end{align*}
$$
c.f. [[Faithful representation]].


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#state/tidy | #lang/en | #SemBr