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Mathematics
Linear and Abstract Algebra
Finitely Generated Modules and Maximal Submodules
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[QUOTE="Math Amateur, post: 5655571, member: 203675"] Well I was thinking of the finite case ... e.g. where for example, \mathcal{C} might be ##N'_1 \subseteq N'_2 \subseteq N'_3## so ... ##N'_3## in this case is an upper bound on the chain ##\mathcal{C}## ... BUT ... your question me me think that my thinking does not cover the case of an infinite chain ... In the case of an infinite chain there may be no largest submodule and so we need to have ##\bigcup_\mathcal{C} N'## as an upper bound ...Can you confirm that my thinking is now correct ... Peter [/QUOTE]
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Forums
Mathematics
Linear and Abstract Algebra
Finitely Generated Modules and Maximal Submodules
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