This type of question comes up quite a lot in past papers, and I'm not sure that we ever learnt how to do it?
MA3G6 Commutative Algebra
Classifying modules up to isomorphism
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No, that topic did not come up a lot in past papers. It only came up in 2011 which I have explicitly said was based on a different syllabus. There was nothing about that in our course, or in the 2012 or 2013 exams, and there will not be this year either. Having said that you may certainly be asked to prove that some isomorphism holds between modules -- but no "classification".0 likes