A field extension that is not algebraic, is said to be transcendental, and must contain transcendental elements, that is, elements that are not algebraic. |
| Алгебраическое расширение |  |
Алгебраи́ческое расшире́ние — расширение поля {\displaystyle \mathbb {E} \supset \mathbb {K} }, где каждый элемент {\displaystyle \alpha \in \mathbb {E} } алгебраичен над {\displaystyle \mathbb {K} }, то есть существует аннулирующий многочлен... Википедия
An extension F of a field K is said to be algebraic if every element of F is algebraic over K (i.e., is the root of a nonzero polynomial with coefficients ... |
9.8 Algebraic extensions. An important class of extensions are those where every element generates a finite extension. Definition 9.8.1. |
In abstract algebra, an algebra extension is the ring-theoretic equivalent of a group extension. Precisely, a ring extension of a ring R by an abelian group ... |
21 мар. 2015 г. · Definition 31.1. An extension field E of field F is an algebraic extension of F if every element in E is algebraic over F. Example. Q ... |
... extension field E of F is called an algebraic extension of F if every element of E is algebraic over F. Otherwise we say it is a transcendental extension of F. |
3 апр. 2018 г. · I think the original motivation for studying field extensions was, as in the theorem you stated, to solve polynomials. Counter-example: any algebraic extension is finite [duplicate] Infinite algebraic extension of Q - Mathematics Stack Exchange E - be an algebraic extension of - F - then - K Algebraic extension which is not finitely generated Другие результаты с сайта math.stackexchange.com |
22 мар. 2013 г. · Let L/K L / K be an extension of fields. L/K L / K is said to be an algebraic extension of fields if every element of L L is algebraic over ... |
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