- #1

steenis

- 312

- 18

Let $M$ be a left $R$-module over a ring $R$.

Let $J$ be a left ideal in $R$ generated by $r$: $J=Rr=<r>$.

Now $JM=\{am \ | \ a \in J \ and \ m \in M\}$

Prove that $JM$ is a submodule of $M$.

This is an example in Rotman's book "Advanced Modern Algebra" 2nd edition 2010, page 404.