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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 wikiPageLength "3325".
- Pure_submodule wikiPageOutDegree "27".
- Pure_submodule wikiPageRevisionID "627025544".
- Pure_submodule wikiPageWikiLink Category:Module_theory.
- Pure_submodule wikiPageWikiLink Direct_limit.
- Pure_submodule wikiPageWikiLink Direct_sum.
- Pure_submodule wikiPageWikiLink Exact_sequence.
- Pure_submodule wikiPageWikiLink Field_(mathematics).
- Pure_submodule wikiPageWikiLink Flat_module.
- Pure_submodule wikiPageWikiLink Injective_function.
- Pure_submodule wikiPageWikiLink Linear_subspace.
- Pure_submodule wikiPageWikiLink Mathematics.
- Pure_submodule wikiPageWikiLink Matrix_(mathematics).
- Pure_submodule wikiPageWikiLink Module_(mathematics).
- Pure_submodule wikiPageWikiLink Projective_module.
- Pure_submodule wikiPageWikiLink Pure_subgroup.
- Pure_submodule wikiPageWikiLink Ring_(mathematics).
- Pure_submodule wikiPageWikiLink Splitting_lemma.
- Pure_submodule wikiPageWikiLink Springer_Science+Business_Media.
- Pure_submodule wikiPageWikiLink Tensor_product.
- Pure_submodule wikiPageWikiLink Vector_space.
- Pure_submodule wikiPageWikiLink Von_Neumann_regular_ring.
- Pure_submodule wikiPageWikiLink File:Short_exact_sequence_ABC.png.
- Pure_submodule wikiPageWikiLinkText "Pure submodule".
- Pure_submodule wikiPageWikiLinkText "pure submodule".
- Pure_submodule wikiPageWikiLinkText "pure".
- Pure_submodule wikiPageUsesTemplate Template:Citation.
- Pure_submodule wikiPageUsesTemplate Template:Harv.
- 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 Q7261159.
- Pure_submodule sameAs m.03njhc.
- Pure_submodule sameAs Q7261159.
- Pure_submodule wasDerivedFrom Pure_submodule?oldid=627025544.
- Pure_submodule depiction Short_exact_sequence_ABC.png.
- Pure_submodule isPrimaryTopicOf Pure_submodule.
