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What can we say about two R-modules, if we know that there supports are equal? What if we know that this modules are Abelian groups? (Z- modules)

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Not much can be said. You will get more useful answers when you add some assumptions and provide some background. –  Martin Brandenburg Feb 13 '13 at 17:32
    
Say they are Abelian groups, and one is the subgroup of another, and again they have equal supports. –  David Feb 13 '13 at 17:42
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Not much can be said. It is best when you really outline the whole situation in which this question occurs. And what you actually want in the end. –  Martin Brandenburg Feb 13 '13 at 17:55

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