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Isomorphism theorems
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===Theorem D (modules)=== Let <math>M</math> be a module, <math>N</math> a submodule of <math>M</math>. There is a bijection between the submodules of <math>M</math> that contain <math>N</math> and the submodules of <math>M/N</math>. The correspondence is given by <math>A\leftrightarrow A/N</math> for all <math>A\supseteq N</math>. This correspondence commutes with the processes of taking sums and intersections (i.e., is a [[lattice isomorphism]] between the lattice of submodules of <math>M/N</math> and the lattice of submodules of <math>M</math> that contain <math>N</math>).<ref>Dummit and Foote (2004), p. 349</ref>
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