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- Algebraic_closure abstract "In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.The algebraic closure of a field K can be thought of as the largest algebraic extension of K.To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K.The algebraic closure of K is also the smallest algebraically closed field containing K,because if M is any algebraically closed field containing K, then the elements of M that are algebraic over K form an algebraic closure of K.The algebraic closure of a field K has the same cardinality as K if K is infinite, and is countably infinite if K is finite.".
- Algebraic_closure wikiPageID "3129".
- Algebraic_closure wikiPageLength "6098".
- Algebraic_closure wikiPageOutDegree "32".
- Algebraic_closure wikiPageRevisionID "653597774".
- Algebraic_closure wikiPageWikiLink Absolute_Galois_group.
- Algebraic_closure wikiPageWikiLink Abstract_algebra.
- Algebraic_closure wikiPageWikiLink Algebraic_extension.
- Algebraic_closure wikiPageWikiLink Algebraic_number.
- Algebraic_closure wikiPageWikiLink Algebraically_closed_field.
- Algebraic_closure wikiPageWikiLink Cardinal_number.
- Algebraic_closure wikiPageWikiLink Category:Field_extensions.
- Algebraic_closure wikiPageWikiLink Closure_(mathematics).
- Algebraic_closure wikiPageWikiLink Complex_number.
- Algebraic_closure wikiPageWikiLink Countable_set.
- Algebraic_closure wikiPageWikiLink Countably_infinite.
- Algebraic_closure wikiPageWikiLink Field_(mathematics).
- Algebraic_closure wikiPageWikiLink Finite_field.
- Algebraic_closure wikiPageWikiLink Fixed_point_(mathematics).
- Algebraic_closure wikiPageWikiLink Fundamental_theorem_of_algebra.
- Algebraic_closure wikiPageWikiLink Integer.
- Algebraic_closure wikiPageWikiLink Isomorphism.
- Algebraic_closure wikiPageWikiLink Mathematics.
- Algebraic_closure wikiPageWikiLink Perfect_field.
- Algebraic_closure wikiPageWikiLink Prime_number.
- Algebraic_closure wikiPageWikiLink Puiseux_expansion.
- Algebraic_closure wikiPageWikiLink Puiseux_series.
- Algebraic_closure wikiPageWikiLink Rational_number.
- Algebraic_closure wikiPageWikiLink Real_number.
- Algebraic_closure wikiPageWikiLink Separable_extension.
- Algebraic_closure wikiPageWikiLink Splitting_field.
- Algebraic_closure wikiPageWikiLink Up_to.
- Algebraic_closure wikiPageWikiLink Zorns_lemma.
- Algebraic_closure wikiPageWikiLinkText "Algebraic closure".
- Algebraic_closure wikiPageWikiLinkText "algebraic closure".
- Algebraic_closure wikiPageWikiLinkText "algebraic closure#Separable closure".
- Algebraic_closure wikiPageWikiLinkText "algebraic".
- Algebraic_closure wikiPageWikiLinkText "algebraically closed".
- Algebraic_closure wikiPageWikiLinkText "algebraically".
- Algebraic_closure wikiPageWikiLinkText "separable closure".
- Algebraic_closure wikiPageWikiLinkText "splitting field for a set of polynomials".
- Algebraic_closure hasPhotoCollection Algebraic_closure.
- Algebraic_closure wikiPageUsesTemplate Template:Cite_book.
- Algebraic_closure wikiPageUsesTemplate Template:Other_uses.
- Algebraic_closure wikiPageUsesTemplate Template:Reflist.
- Algebraic_closure subject Category:Field_extensions.
- Algebraic_closure hypernym Extension.
- Algebraic_closure type Article.
- Algebraic_closure type Software.
- Algebraic_closure type Article.
- Algebraic_closure comment "In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K.".
- Algebraic_closure label "Algebraic closure".
- Algebraic_closure sameAs Algebraický_uzávěr.
- Algebraic_closure sameAs Algebraischer_Abschluss.
- Algebraic_closure sameAs Tegaĵo.
- Algebraic_closure sameAs Clausura_algebraica.
- Algebraic_closure sameAs Algebrallinen_sulkeuma.
- Algebraic_closure sameAs Clôture_algébrique.
- Algebraic_closure sameAs סגור_אלגברי.
- Algebraic_closure sameAs Chiusura_algebrica.
- Algebraic_closure sameAs 代数的閉包.
- Algebraic_closure sameAs 대수적_폐포.
- Algebraic_closure sameAs Gesloten_(algebra).
- Algebraic_closure sameAs Fecho_algébrico.
- Algebraic_closure sameAs m.013wh.
- Algebraic_closure sameAs Q428290.
- Algebraic_closure sameAs Q428290.
- Algebraic_closure wasDerivedFrom Algebraic_closure?oldid=653597774.
- Algebraic_closure isPrimaryTopicOf Algebraic_closure.