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- Transcendence_degree abstract "In abstract algebra, the transcendence degree of a field extension L /K is a certain rather coarse measure of the "size" of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K.A subset S of L is a transcendence basis of L /K if it is algebraically independent over K and if furthermore L is an algebraic extension of the field K(S) (the field obtained by adjoining the elements of S to K). One can show that every field extension has a transcendence basis, and that all transcendence bases have the same cardinality; this cardinality is equal to the transcendence degree of the extension and is denoted trdegK L or trdeg(L /K).If no field K is specified, the transcendence degree of a field L is its degree relative to the prime field of the same characteristic, i.e., Q if L is of characteristic 0 and Fp if L is of characteristic p.The field extension L /K is purely transcendental if there is a subset S of L that is algebraically independent over K and such that L = K(S).".
- Transcendence_degree wikiPageID "287364".
- Transcendence_degree wikiPageLength "6486".
- Transcendence_degree wikiPageOutDegree "40".
- Transcendence_degree wikiPageRevisionID "621668228".
- Transcendence_degree wikiPageWikiLink Abstract_algebra.
- Transcendence_degree wikiPageWikiLink Algebraic_closure.
- Transcendence_degree wikiPageWikiLink Algebraic_extension.
- Transcendence_degree wikiPageWikiLink Algebraic_independence.
- Transcendence_degree wikiPageWikiLink Algebraic_number.
- Transcendence_degree wikiPageWikiLink Algebraic_variety.
- Transcendence_degree wikiPageWikiLink Algebraically_closed.
- Transcendence_degree wikiPageWikiLink Algebraically_closed_field.
- Transcendence_degree wikiPageWikiLink Algebraically_independent.
- Transcendence_degree wikiPageWikiLink Automorphism.
- Transcendence_degree wikiPageWikiLink Axiom_of_choice.
- Transcendence_degree wikiPageWikiLink Basis_(linear_algebra).
- Transcendence_degree wikiPageWikiLink Cardinality.
- Transcendence_degree wikiPageWikiLink Carl_Ludwig_Siegel.
- Transcendence_degree wikiPageWikiLink Category:Algebraic_varieties.
- Transcendence_degree wikiPageWikiLink Category:Field_theory.
- Transcendence_degree wikiPageWikiLink Category:Matroid_theory.
- Transcendence_degree wikiPageWikiLink Category:Transcendental_numbers.
- Transcendence_degree wikiPageWikiLink Characteristic_(algebra).
- Transcendence_degree wikiPageWikiLink Complex_number.
- Transcendence_degree wikiPageWikiLink Continuum_hypothesis.
- Transcendence_degree wikiPageWikiLink Dimension_(vector_space).
- Transcendence_degree wikiPageWikiLink E_(mathematical_constant).
- Transcendence_degree wikiPageWikiLink Empty_set.
- Transcendence_degree wikiPageWikiLink Exchange_lemma.
- Transcendence_degree wikiPageWikiLink Field_extension.
- Transcendence_degree wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Transcendence_degree wikiPageWikiLink Hamel_dimension.
- Transcendence_degree wikiPageWikiLink Injective.
- Transcendence_degree wikiPageWikiLink Injective_function.
- Transcendence_degree wikiPageWikiLink Linear_independence.
- Transcendence_degree wikiPageWikiLink Linear_span.
- Transcendence_degree wikiPageWikiLink Matroid.
- Transcendence_degree wikiPageWikiLink Matroid_rank.
- Transcendence_degree wikiPageWikiLink Meromorphic_function.
- Transcendence_degree wikiPageWikiLink Pi.
- Transcendence_degree wikiPageWikiLink Prime_field.
- Transcendence_degree wikiPageWikiLink Square_root_of_2.
- Transcendence_degree wikiPageWikiLink Square_root_of_two.
- Transcendence_degree wikiPageWikiLink Steinitz_exchange_lemma.
- Transcendence_degree wikiPageWikiLink Subset.
- Transcendence_degree wikiPageWikiLink Surjective.
- Transcendence_degree wikiPageWikiLink Surjective_function.
- Transcendence_degree wikiPageWikiLink Transcendental_number.
- Transcendence_degree wikiPageWikiLink Union_(set_theory).
- Transcendence_degree wikiPageWikiLink Vector_space.
- Transcendence_degree wikiPageWikiLinkText "Transcendence degree".
- Transcendence_degree wikiPageWikiLinkText "transcendence degree".
- Transcendence_degree hasPhotoCollection Transcendence_degree.
- Transcendence_degree subject Category:Algebraic_varieties.
- Transcendence_degree subject Category:Field_theory.
- Transcendence_degree subject Category:Matroid_theory.
- Transcendence_degree subject Category:Transcendental_numbers.
- Transcendence_degree type Combinatoric.
- Transcendence_degree type Variety.
- Transcendence_degree comment "In abstract algebra, the transcendence degree of a field extension L /K is a certain rather coarse measure of the "size" of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K.A subset S of L is a transcendence basis of L /K if it is algebraically independent over K and if furthermore L is an algebraic extension of the field K(S) (the field obtained by adjoining the elements of S to K).".
- Transcendence_degree label "Transcendence degree".
- Transcendence_degree sameAs Transzendenzbasis.
- Transcendence_degree sameAs 超越次数.
- Transcendence_degree sameAs Grau_de_transcendência.
- Transcendence_degree sameAs m.01q61x.
- Transcendence_degree sameAs Степінь_трансцендентності.
- Transcendence_degree sameAs Q1387602.
- Transcendence_degree sameAs Q1387602.
- Transcendence_degree sameAs 超越次數.
- Transcendence_degree wasDerivedFrom Transcendence_degree?oldid=621668228.
- Transcendence_degree isPrimaryTopicOf Transcendence_degree.