Question

Show that every submodule of a finitely generated module over a P.I.D.
is finitely generated.
rifond only if it is direct​

Answer 1

Step-by-step explanation:

In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groupsand roughly states that finitely generated modules over a principal ideal domain can be uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical form results for square matrices over fields.

Answer 2

Step by step axplaination i solve hope it will help you.