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- Uniform_module abstract "In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that every nonzero submodule of M is an essential submodule. A ring may be called a right (left) uniform ring if it is uniform as a right (left) module over itself. Alfred Goldie used the notion of uniform modules to construct a measure of dimension for modules, now known as the uniform dimension (or Goldie dimension) of a module. Uniform dimension generalizes some, but not all, aspects of the notion of the dimension of a vector space. Finite uniform dimension was a key assumption for several theorems by Goldie, including Goldie's theorem, which characterizes which rings are right orders in a semisimple ring. Modules of finite uniform dimension generalize both Artinian modules and Noetherian modules.In the literature, uniform dimension is also referred to as simply the dimension of a module or the rank of a module. Uniform dimension should not be confused with the related notion, also due to Goldie, of the reduced rank of a module.".
- Uniform_module wikiPageID "31553078".
- Uniform_module wikiPageLength "9564".
- Uniform_module wikiPageOutDegree "29".
- Uniform_module wikiPageRevisionID "627091004".
- Uniform_module wikiPageWikiLink Abstract_algebra.
- Uniform_module wikiPageWikiLink Alfred_Goldie.
- Uniform_module wikiPageWikiLink Artinian_module.
- Uniform_module wikiPageWikiLink Category:Module_theory.
- Uniform_module wikiPageWikiLink Category:Ring_theory.
- Uniform_module wikiPageWikiLink Communications_in_Algebra.
- Uniform_module wikiPageWikiLink Composition_series.
- Uniform_module wikiPageWikiLink Dimension.
- Uniform_module wikiPageWikiLink Dimension_(vector_space).
- Uniform_module wikiPageWikiLink Duality_(mathematics).
- Uniform_module wikiPageWikiLink Essential_extension.
- Uniform_module wikiPageWikiLink Finitely_generated_module.
- Uniform_module wikiPageWikiLink Goldies_theorem.
- Uniform_module wikiPageWikiLink Injective_hull.
- Uniform_module wikiPageWikiLink Injective_module.
- Uniform_module wikiPageWikiLink Noetherian_module.
- Uniform_module wikiPageWikiLink Ore_condition.
- Uniform_module wikiPageWikiLink Reduced_rank.
- Uniform_module wikiPageWikiLink Right_order.
- Uniform_module wikiPageWikiLink Semi-local_ring.
- Uniform_module wikiPageWikiLink Semisimple_module.
- Uniform_module wikiPageWikiLink Serial_module.
- Uniform_module wikiPageWikiLink Springer_Science+Business_Media.
- Uniform_module wikiPageWikiLinkText "co-uniform dimension".
- Uniform_module wikiPageWikiLinkText "reduced rank".
- Uniform_module wikiPageWikiLinkText "uniform dimension".
- Uniform_module wikiPageWikiLinkText "uniform module".
- Uniform_module wikiPageWikiLinkText "uniform module#Hollow modules and co-uniform dimension".
- Uniform_module wikiPageUsesTemplate Template:Citation.
- Uniform_module wikiPageUsesTemplate Template:Harv.
- Uniform_module wikiPageUsesTemplate Template:Reflist.
- Uniform_module subject Category:Module_theory.
- Uniform_module subject Category:Ring_theory.
- Uniform_module hypernym Nonzero.
- Uniform_module comment "In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that every nonzero submodule of M is an essential submodule. A ring may be called a right (left) uniform ring if it is uniform as a right (left) module over itself. Alfred Goldie used the notion of uniform modules to construct a measure of dimension for modules, now known as the uniform dimension (or Goldie dimension) of a module.".
- Uniform_module label "Uniform module".
- Uniform_module sameAs Q7885110.
- Uniform_module sameAs 一様加群.
- Uniform_module sameAs m.0gtx4by.
- Uniform_module sameAs Q7885110.
- Uniform_module wasDerivedFrom Uniform_module?oldid=627091004.
- Uniform_module isPrimaryTopicOf Uniform_module.