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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 wikiPageRevisionID "541208390".
- 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 Abstraction100002137.
- Transcendence_degree type AlgebraicVarieties.
- Transcendence_degree type Assortment108398773.
- Transcendence_degree type Collection107951464.
- Transcendence_degree type Group100031264.
- 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 "Grau de transcendência".
- Transcendence_degree label "Transcendence degree".
- Transcendence_degree label "Transzendenzbasis".
- Transcendence_degree label "超越次數".
- Transcendence_degree sameAs Transzendenzbasis.
- Transcendence_degree sameAs Grau_de_transcendência.
- Transcendence_degree sameAs m.01q61x.
- Transcendence_degree sameAs Q1387602.
- Transcendence_degree sameAs Q1387602.
- Transcendence_degree sameAs Transcendence_degree.
- Transcendence_degree wasDerivedFrom Transcendence_degree?oldid=541208390.
- Transcendence_degree isPrimaryTopicOf Transcendence_degree.