Let $M$ be a not necessarily free module over a commutative unital ring. True or false: if every linear form assigns to a vector of $M$ zero, then the vector is the zero vector?
Counterexample: $R=\mathbb Z$ and $M=\mathbb Z/2$. 


Let $M$ be a not necessarily free module over a commutative unital ring. True or false: if every linear form assigns to a vector of $M$ zero, then the vector is the zero vector? 


Counterexample: $R=\mathbb Z$ and $M=\mathbb Z/2$. 

