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- Top_(mathematics) abstract "In the context of a module M over a ring R, the top of M is the largest semisimple quotient module of M if it exists. For finite-dimensional k-algebras (k a field), if rad(M) denotes the intersection of all proper maximal submodules of M (the radical of the module), then the top of M is M/rad(M). In the case of local rings with maximal ideal P, the top of M is M/PM. In general if R is a semilocal ring (=semi-artinian ring), that is, if R/Rad(R) is an Artinian ring, where Rad(R) is the Jacobson radical of R, then M/rad(M) is a semisimple module and is the top of M. This includes the cases of local rings and finite dimensional algebras over fields.".
- Top_(mathematics) wikiPageID "21094724".
- Top_(mathematics) wikiPageLength "1165".
- Top_(mathematics) wikiPageOutDegree "15".
- Top_(mathematics) wikiPageRevisionID "468906254".
- Top_(mathematics) wikiPageWikiLink Artinian_ring.
- Top_(mathematics) wikiPageWikiLink Category:Commutative_algebra.
- Top_(mathematics) wikiPageWikiLink Category:Module_theory.
- Top_(mathematics) wikiPageWikiLink David_Eisenbud.
- Top_(mathematics) wikiPageWikiLink Jacobson_radical.
- Top_(mathematics) wikiPageWikiLink Maximal_ideal.
- Top_(mathematics) wikiPageWikiLink Module_(mathematics).
- Top_(mathematics) wikiPageWikiLink Projective_cover.
- Top_(mathematics) wikiPageWikiLink Quotient_module.
- Top_(mathematics) wikiPageWikiLink Radical_of_a_module.
- Top_(mathematics) wikiPageWikiLink Ring_(mathematics).
- Top_(mathematics) wikiPageWikiLink Semi-local_ring.
- Top_(mathematics) wikiPageWikiLink Semisimple_module.
- Top_(mathematics) wikiPageWikiLink Socle_(mathematics).
- Top_(mathematics) wikiPageWikiLinkText "Top (mathematics)".
- Top_(mathematics) wikiPageWikiLinkText "top".
- Top_(mathematics) wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Top_(mathematics) subject Category:Commutative_algebra.
- Top_(mathematics) subject Category:Module_theory.
- Top_(mathematics) hypernym Module.
- Top_(mathematics) type Software.
- Top_(mathematics) comment "In the context of a module M over a ring R, the top of M is the largest semisimple quotient module of M if it exists. For finite-dimensional k-algebras (k a field), if rad(M) denotes the intersection of all proper maximal submodules of M (the radical of the module), then the top of M is M/rad(M). In the case of local rings with maximal ideal P, the top of M is M/PM.".
- Top_(mathematics) label "Top (mathematics)".
- Top_(mathematics) sameAs Q7824391.
- Top_(mathematics) sameAs m.05c3l15.
- Top_(mathematics) sameAs Q7824391.
- Top_(mathematics) wasDerivedFrom Top_(mathematics)?oldid=468906254.
- Top_(mathematics) isPrimaryTopicOf Top_(mathematics).