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- Pure_submodule abstract "In mathematics, especially in the field of module theory, the concept of pure submodule provides a generalization of direct summand, a type of particularly well-behaved piece of a module. Pure modules are complementary to flat modules and generalize Prüfer's notion of pure subgroups. While flat modules are those modules which leave short exact sequences exact after tensoring, a pure submodule defines a short exact sequence that remains exact after tensoring with any module. Similarly a flat module is a direct limit of projective modules, and a pure submodule defines a short exact sequence which is a direct limit of split exact sequences, each defined by a direct summand.".
- Pure_submodule thumbnail Short_exact_sequence_ABC.png?width=300.
- Pure_submodule wikiPageID "904490".
- Pure_submodule wikiPageRevisionID "512926834".
- Pure_submodule hasPhotoCollection Pure_submodule.
- Pure_submodule subject Category:Module_theory.
- Pure_submodule comment "In mathematics, especially in the field of module theory, the concept of pure submodule provides a generalization of direct summand, a type of particularly well-behaved piece of a module. Pure modules are complementary to flat modules and generalize Prüfer's notion of pure subgroups. While flat modules are those modules which leave short exact sequences exact after tensoring, a pure submodule defines a short exact sequence that remains exact after tensoring with any module.".
- Pure_submodule label "Pure submodule".
- Pure_submodule sameAs m.03njhc.
- Pure_submodule sameAs Q7261159.
- Pure_submodule sameAs Q7261159.
- Pure_submodule wasDerivedFrom Pure_submodule?oldid=512926834.
- Pure_submodule depiction Short_exact_sequence_ABC.png.
- Pure_submodule isPrimaryTopicOf Pure_submodule.
