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I am unable to write this is in comments. While this is not an answer to your question, a similar structure theorem holds for Principal ideal rings (which are just Artin rings) where every finitely generated module is isomorphic to a direct sum of cyclic modules. http://www.iecn.u-nancy.fr/~gaillard/DIVERS/Principal.ideals/principal.ideals.070702.pdf |
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I am unable to write this is in comments. While this is not an answer to your question, a similar structure theorem holds for Principal ideal rings (which are just Artin rings) where every finitely generated module is isomorphic to a direct sum of cyclic modules. http://www.iecn.u-nancy.fr/~gaillard/DIVERS/Principal.ideals/principal.ideals.070702.pdf |
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