Question: Please help to solve this Group Theory question. Detailed steps are required. Thanks! Let A be a principal ideal domain, and let K := Frac(

Please help to solve this Group Theory question. Detailed steps are required. Thanks!

Let A be a principal ideal domain, and let K := Frac( A) be its field of fractions. Regard K as an A-module via the inclusion ring homomorphism A > K. Let M C K be any finitely generated A-submodule of K . Show that either M is the zero A-module, or M is isomorphic to A as an A-module

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