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6 definitions found
From English Wiktionary: All languages (2023-07-27) : [ dictinfo.com:wikt-en-ALL-2023-07-27 ]
algebraic closure
n.
(lb en algebra field theory of a field ''F'') A field ''G'' such that
every polynomial over ''F'' splits completely over ''G'' (i.e., every
element of ''G'' is a root of some polynomial over ''F'' and every root
of every polynomial over ''F'' is an element of ''G'').
From English Wiktionary: English language only (2023-07-27) : [ dictinfo.com:wikt-en-en-2023-07-27 ]
algebraic closure
n.
(lb en algebra field theory of a field ''F'') A field ''G'' such that
every polynomial over ''F'' splits completely over ''G'' (i.e., every
element of ''G'' is a root of some polynomial over ''F'' and every root
of every polynomial over ''F'' is an element of ''G'').
From English Wiktionary: Western, Greek, and Slavonic languages only (2023-07-27) : [ dictinfo.com:wikt-en-Western_Greek_Slavonic-2023-07-27 ]
algebraic closure
n.
(lb en algebra field theory of a field ''F'') A field ''G'' such that
every polynomial over ''F'' splits completely over ''G'' (i.e., every
element of ''G'' is a root of some polynomial over ''F'' and every root
of every polynomial over ''F'' is an element of ''G'').
From English Wiktionary: Western languages only (2023-07-27) : [ dictinfo.com:wikt-en-Western-2023-07-27 ]
algebraic closure
n.
(lb en algebra field theory of a field ''F'') A field ''G'' such that
every polynomial over ''F'' splits completely over ''G'' (i.e., every
element of ''G'' is a root of some polynomial over ''F'' and every root
of every polynomial over ''F'' is an element of ''G'').
From English - German Ding/FreeDict dictionary ver. 1.9-fd1 : [ freedict:eng-deu ]
algebraic closure /ˌaldʒɪbɹˈeɪɪk klˈəʊʒə/
algebraische Hülle
Synonym: algebraic hull
see: algebraic, algebraic function, algebraic geometry, algebraic equation, algebraic complement, algebraic structure, algebraic number
From English-suomi FreeDict+WikDict dictionary ver. 2023.05.29 : [ freedict:eng-fin ]
algebraic closure /ˌaldʒɪbɹˈeɪɪk klˈəʊʒə/
algebrallinen sulkeuma
field which is algebraically closed over another one
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