1. The problem statement, all variables and given/known data I am curious if all modules contain 0. 2. Relevant equations A left R-module M over the ring R consists of an abelian group (M, +) and an operation R × M → M such that certain properties hold... 3. The attempt at a solution The definition of a module says that it is an additive group, and additive groups have the zero element. Thus, all modules contain the zero element right? Thank you.