Solution
= Solution
If $cI\subset R$, then $cI$ is an <ideal> of the Noetherian <ring> $R$, hence finitely generated; scaling back shows $I$ is finitely generated.
= Solution
If $cI\subset R$, then $cI$ is an <ideal> of the Noetherian <ring> $R$, hence finitely generated; scaling back shows $I$ is finitely generated.