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- Rank_of_an_abelian_group abstract "In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained in A. If A is torsion-free then it embeds into a vector space over the rational numbers of dimension rank A. For finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup. Torsion-free abelian groups of rank 1 have been completely classified. However, the theory of abelian groups of higher rank is more involved.The term rank has a different meaning in the context of elementary abelian groups.".
- Rank_of_an_abelian_group wikiPageID "244541".
- Rank_of_an_abelian_group wikiPageLength "7110".
- Rank_of_an_abelian_group wikiPageOutDegree "35".
- Rank_of_an_abelian_group wikiPageRevisionID "636831411".
- Rank_of_an_abelian_group wikiPageWikiLink Abelian_group.
- Rank_of_an_abelian_group wikiPageWikiLink Cardinal_arithmetic.
- Rank_of_an_abelian_group wikiPageWikiLink Cardinal_number.
- Rank_of_an_abelian_group wikiPageWikiLink Cardinality.
- Rank_of_an_abelian_group wikiPageWikiLink Category:Abelian_group_theory.
- Rank_of_an_abelian_group wikiPageWikiLink Dimension_(vector_space).
- Rank_of_an_abelian_group wikiPageWikiLink Direct_sum.
- Rank_of_an_abelian_group wikiPageWikiLink Elementary_abelian_group.
- Rank_of_an_abelian_group wikiPageWikiLink Exact_sequence.
- Rank_of_an_abelian_group wikiPageWikiLink Field_of_fractions.
- Rank_of_an_abelian_group wikiPageWikiLink Finitely_generated_abelian_group.
- Rank_of_an_abelian_group wikiPageWikiLink Flat_module.
- Rank_of_an_abelian_group wikiPageWikiLink Free_abelian_group.
- Rank_of_an_abelian_group wikiPageWikiLink Indecomposable_module.
- Rank_of_an_abelian_group wikiPageWikiLink Injective.
- Rank_of_an_abelian_group wikiPageWikiLink Injective_function.
- Rank_of_an_abelian_group wikiPageWikiLink Integral_domain.
- Rank_of_an_abelian_group wikiPageWikiLink Linear_independence.
- Rank_of_an_abelian_group wikiPageWikiLink Linearly_independent.
- Rank_of_an_abelian_group wikiPageWikiLink Mathematics.
- Rank_of_an_abelian_group wikiPageWikiLink Module_(mathematics).
- Rank_of_an_abelian_group wikiPageWikiLink Order_(group_theory).
- Rank_of_an_abelian_group wikiPageWikiLink Periodic_group.
- Rank_of_an_abelian_group wikiPageWikiLink Quotient_field.
- Rank_of_an_abelian_group wikiPageWikiLink Rank_of_a_group.
- Rank_of_an_abelian_group wikiPageWikiLink Rational_number.
- Rank_of_an_abelian_group wikiPageWikiLink Rational_numbers.
- Rank_of_an_abelian_group wikiPageWikiLink Short_exact_sequence.
- Rank_of_an_abelian_group wikiPageWikiLink Tensor_product.
- Rank_of_an_abelian_group wikiPageWikiLink Torsion-free_abelian_groups_of_rank_1.
- Rank_of_an_abelian_group wikiPageWikiLink Torsion_(algebra).
- Rank_of_an_abelian_group wikiPageWikiLink Torsion_group.
- Rank_of_an_abelian_group wikiPageWikiLink Torsion_subgroup.
- Rank_of_an_abelian_group wikiPageWikiLink Vector_space.
- Rank_of_an_abelian_group wikiPageWikiLink Vector_space_dimension.
- Rank_of_an_abelian_group wikiPageWikiLinkText "Rank of an abelian group".
- Rank_of_an_abelian_group wikiPageWikiLinkText "Rank_of_an_abelian_group".
- Rank_of_an_abelian_group wikiPageWikiLinkText "rank of abelian groups".
- Rank_of_an_abelian_group wikiPageWikiLinkText "rank of an abelian group".
- Rank_of_an_abelian_group wikiPageWikiLinkText "rank".
- Rank_of_an_abelian_group wikiPageWikiLinkText "rank-2".
- Rank_of_an_abelian_group wikiPageWikiLinkText "ranks".
- Rank_of_an_abelian_group hasPhotoCollection Rank_of_an_abelian_group.
- Rank_of_an_abelian_group wikiPageUsesTemplate Template:Citation_needed.
- Rank_of_an_abelian_group wikiPageUsesTemplate Template:Refimprove.
- Rank_of_an_abelian_group wikiPageUsesTemplate Template:Reflist.
- Rank_of_an_abelian_group subject Category:Abelian_group_theory.
- Rank_of_an_abelian_group hypernym Cardinality.
- Rank_of_an_abelian_group type Article.
- Rank_of_an_abelian_group type Article.
- Rank_of_an_abelian_group comment "In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained in A. If A is torsion-free then it embeds into a vector space over the rational numbers of dimension rank A. For finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup.".
- Rank_of_an_abelian_group label "Rank of an abelian group".
- Rank_of_an_abelian_group sameAs Rang_einer_abelschen_Gruppe.
- Rank_of_an_abelian_group sameAs Aste_(Abelin_ryhmä).
- Rank_of_an_abelian_group sameAs アーベル群のランク.
- Rank_of_an_abelian_group sameAs 계수_(아벨_군).
- Rank_of_an_abelian_group sameAs Ranga_grupy_abelowej.
- Rank_of_an_abelian_group sameAs Ordem_de_um_grupo_abeliano.
- Rank_of_an_abelian_group sameAs m.01kf4r.
- Rank_of_an_abelian_group sameAs Q1260803.
- Rank_of_an_abelian_group sameAs Q1260803.
- Rank_of_an_abelian_group wasDerivedFrom Rank_of_an_abelian_group?oldid=636831411.
- Rank_of_an_abelian_group isPrimaryTopicOf Rank_of_an_abelian_group.