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- Algebraic_independence abstract "In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K. In particular, a one element set {α} is algebraically independent over K if and only if α is transcendental over K. In general, all the elements of an algebraically independent set S over K are by necessity transcendental over K, and over all of the field extensions over K generated by the remaining elements of S.".
- Algebraic_independence wikiPageID "287808".
- Algebraic_independence wikiPageLength "6068".
- Algebraic_independence wikiPageOutDegree "31".
- Algebraic_independence wikiPageRevisionID "561258880".
- Algebraic_independence wikiPageWikiLink Abstract_algebra.
- Algebraic_independence wikiPageWikiLink Algebraic_element.
- Algebraic_independence wikiPageWikiLink Algebraic_number.
- Algebraic_independence wikiPageWikiLink Cardinality.
- Algebraic_independence wikiPageWikiLink Category:Abstract_algebra.
- Algebraic_independence wikiPageWikiLink Category:Matroid_theory.
- Algebraic_independence wikiPageWikiLink E_(mathematical_constant).
- Algebraic_independence wikiPageWikiLink Field_(mathematics).
- Algebraic_independence wikiPageWikiLink Field_extension.
- Algebraic_independence wikiPageWikiLink Gamma_function.
- Algebraic_independence wikiPageWikiLink If_and_only_if.
- Algebraic_independence wikiPageWikiLink Indeterminate_(variable).
- Algebraic_independence wikiPageWikiLink Lindemann–Weierstrass_theorem.
- Algebraic_independence wikiPageWikiLink Linear_independence.
- Algebraic_independence wikiPageWikiLink Matrix_(mathematics).
- Algebraic_independence wikiPageWikiLink Matroid.
- Algebraic_independence wikiPageWikiLink Matroid_representation.
- Algebraic_independence wikiPageWikiLink Polynomial.
- Algebraic_independence wikiPageWikiLink Rational_number.
- Algebraic_independence wikiPageWikiLink Real_number.
- Algebraic_independence wikiPageWikiLink Singleton_(mathematics).
- Algebraic_independence wikiPageWikiLink Subset.
- Algebraic_independence wikiPageWikiLink Transcendence_degree.
- Algebraic_independence wikiPageWikiLink Transcendental_number.
- Algebraic_independence wikiPageWikiLink Triviality_(mathematics).
- Algebraic_independence wikiPageWikiLink Vámos_matroid.
- Algebraic_independence wikiPageWikiLink Yuri_Valentinovich_Nesterenko.
- Algebraic_independence wikiPageWikiLink Zorns_lemma.
- Algebraic_independence wikiPageWikiLinkText "''algebraic'' independence".
- Algebraic_independence wikiPageWikiLinkText "Algebraic independence".
- Algebraic_independence wikiPageWikiLinkText "algebraic independence".
- Algebraic_independence wikiPageWikiLinkText "algebraically independent".
- Algebraic_independence author "Chen, Johnny".
- Algebraic_independence title "Algebraically Independent".
- Algebraic_independence urlname "AlgebraicallyIndependent".
- Algebraic_independence wikiPageUsesTemplate Template:Main.
- Algebraic_independence wikiPageUsesTemplate Template:MathWorld.
- Algebraic_independence wikiPageUsesTemplate Template:Reflist.
- Algebraic_independence subject Category:Abstract_algebra.
- Algebraic_independence subject Category:Matroid_theory.
- Algebraic_independence hypernym Transcendental.
- Algebraic_independence type Combinatoric.
- Algebraic_independence comment "In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K. In particular, a one element set {α} is algebraically independent over K if and only if α is transcendental over K.".
- Algebraic_independence label "Algebraic independence".
- Algebraic_independence sameAs Q1495342.
- Algebraic_independence sameAs استقلال_جبري.
- Algebraic_independence sameAs Algebraická_nezávislost.
- Algebraic_independence sameAs Algebraische_Unabhängigkeit.
- Algebraic_independence sameAs Independencia_algebraica.
- Algebraic_independence sameAs Indépendance_algébrique.
- Algebraic_independence sameAs אי_תלות_אלגברית.
- Algebraic_independence sameAs Indipendenza_algebrica.
- Algebraic_independence sameAs Algebraïsche_onafhankelijkheid.
- Algebraic_independence sameAs Independência_algébrica.
- Algebraic_independence sameAs m.01q7rk.
- Algebraic_independence sameAs Алгебраическая_независимость.
- Algebraic_independence sameAs Algebrická_nezávislosť.
- Algebraic_independence sameAs Алгебраїчна_незалежність.
- Algebraic_independence sameAs Q1495342.
- Algebraic_independence sameAs 代數獨立.
- Algebraic_independence wasDerivedFrom Algebraic_independence?oldid=561258880.
- Algebraic_independence isPrimaryTopicOf Algebraic_independence.