2021-29.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	29	IB 2021 Groups, Rings and Modules	Paper 2, Section I, $1 G$	2021

Let $M$ be a module over a Principal Ideal Domain $R$ and let $N$ be a submodule of $M$. Show that $M$ is finitely generated if and only if $N$ and $M / N$ are finitely generated.