algebraic closure
algebraic closure · algebraic closures
A field G such that every polynomial over F splits completely over GA 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).
Meaning
1 sensesA 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).
Translations
3 languagesForms
plural: algebraic closures| Singular | algebraic closure |
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| Plural | algebraic closures |
regular
Word family
1 related wordsRelatedalgebraically closed
See also
neighbours in the dictionaryDictionary text adapted from Wiktionary (Wiktionary contributors, CC BY-SA 4.0) and Open English WordNet / Princeton WordNet (CC BY 4.0, WordNet License); shared under CC BY-SA 4.0. Example sentences and recordings are credited where they appear.