2017-34.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	34	IB 2017 Groups, Rings and Modules	Paper 4, Section II, E	2017

(a) State (without proof) the classification theorem for finitely generated modules over a Euclidean domain. Give the statement and the proof of the rational canonical form theorem.

(b) Let $R$ be a principal ideal domain and let $M$ be an $R$-submodule of $R^{n}$. Show that $M$ is a free $R$-module.