Prove that any finitely related module may be expressed as the direct sum of a finitely presented module and a free module.
Hint: If M is generated by X = X' U X'', where X' is the finite subset of X involved in the defining relations, then M is the direct sum of :
- the free module over X''
- the module generated by X' with the defining relations for M
How do I prove that the module generated by X' is finitely presented?
How do I prove that the direct sum of these modules is M?