Faithful module

A (left) $𝑅$ -module $𝑉$ is said to be (left) faithful iff the Annihilator $𝑅 A n n 𝑉 = 0$ is trivial, module i.e. for any $𝑟 \in 𝑅$

𝑟 ⊙ 𝑉 = 0 ⟺ 𝑟 = 0 .