Share
Explore BrainMass

Modules, Submodules, Commutative Rings with Unity and Homomorphism

1. Let R and S be commutative rings with unity, and let φ: R S be a ring homomorphism. If M is an S-module, prove that M is also an R-module if we define rm = φ(r)m for all r E R and m E M.

2. If M1 and M2 are submodules of an R-module M such that M = M1(+)M2, prove that M1 = M/M2 and M2 = M/M1.

Attachments

Solution Summary

Modules, Submodules , Commutative Rings with Unity and Homomorphism are investigated.

$2.19