Let R be a commutative ring and let J be an Ideal in R. Recall That if M is an R-Module, then JM= { sum j_{i}m_{i}} is a submodule of M. Prove that M/JM is an R/J module if we define scalar multiplication: (r+J)(m+JM) = rm + JM.

Conclude that If JM ={0}, then M itself is an R/J module. IF J is maximal ideal in R, then M is a vetor space over R/J.