Thread: Modules

Let R and S be commutative rings and let phi: R to S be a ring homomorphism.

If M is an S-Module, prove that M is also and R-Module if we define rm = phi(r)m.
for all r in R and all m in M.

Originally Posted by jcir2826

Let R and S be commutative rings and let phi: R to S be a ring homomorphism.If M is an S-Module, prove that M is also and R-Module if we define rm = phi(r)m. for all r in R and all m in M.

It is an easy consequence of the corresponding definitions:





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Try the rest.