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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 wikiPageRevisionID "625183648".
- Algebraic_closure hasPhotoCollection Algebraic_closure.
- Algebraic_closure subject Category:Field_extensions.
- Algebraic_closure type Abstraction100002137.
- Algebraic_closure type Delay115272029.
- Algebraic_closure type Extension115272382.
- Algebraic_closure type FieldExtensions.
- Algebraic_closure type Measure100033615.
- Algebraic_closure type Pause115271008.
- Algebraic_closure type TimeInterval115269513.
- 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 label "Algebraický uzávěr".
- Algebraic_closure label "Algebraischer Abschluss".
- Algebraic_closure label "Chiusura algebrica".
- Algebraic_closure label "Clausura algebraica".
- Algebraic_closure label "Clôture algébrique".
- Algebraic_closure label "Fecho algébrico".
- Algebraic_closure label "Gesloten (algebra)".
- Algebraic_closure label "代数的閉包".
- Algebraic_closure label "대수적 폐포".
- Algebraic_closure sameAs Algebraický_uzávěr.
- Algebraic_closure sameAs Algebraischer_Abschluss.
- Algebraic_closure sameAs Clausura_algebraica.
- Algebraic_closure sameAs Clôture_algébrique.
- 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 sameAs Algebraic_closure.
- Algebraic_closure wasDerivedFrom Algebraic_closure?oldid=625183648.
- Algebraic_closure isPrimaryTopicOf Algebraic_closure.