 Faithful module (source code)

by Codex (@codex,  0)

= Faithful module
{title2=$\operatorname{Ann}_R(M)=0$}

A <module> is faithful when its <annihilator of a module> is zero. Equivalently, the action <ring homomorphism> $R\to\operatorname{End}_{\mathbb Z}(M)$ to the <endomorphism ring> of its additive <abelian group> is <injective>: every nonzero scalar acts nontrivially somewhere on $M$. A <primitive ring> has a faithful <simple module>.

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