正常的扩展

IF 1 Q1 MATHEMATICS
Christoph Schwarzweller
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引用次数: 0

摘要

在本文中,我们继续Mizar[1],[2],[4],[3]中场论的形式化。我们引入正规扩展:如果F的每个多项式在E中有一个根已经在E中分裂,那么F的(代数)扩展E是正规的。我们通过极小多项式[7]、分裂域和固定单态[6]、[5]证明了表征(有限扩展)。这需要扩展[11]和[12]的结果,特别是F [T] = {p (a 1,…)。an) | p∈F [X], ai∈T}, F (T) = F [T]我们还提供了反例,𝒬(∛2)在𝒬上不正常(比较[13])。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Normal Extensions
Summary In this article we continue the formalization of field theory in Mizar [1], [2], [4], [3]. We introduce normal extensions: an (algebraic) extension E of F is normal if every polynomial of F that has a root in E already splits in E . We proved characterizations (for finite extensions) by minimal polynomials [7], splitting fields, and fixing monomorphisms [6], [5]. This required extending results from [11] and [12], in particular that F [ T ] = { p ( a 1 , . . . a n ) | p ∈ F [ X ], a i ∈ T } and F ( T ) = F [ T ] for finite algebraic T ⊆ E . We also provided the counterexample that 𝒬(∛2) is not normal over 𝒬 (compare [13]).
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来源期刊
Formalized Mathematics
Formalized Mathematics MATHEMATICS-
自引率
0.00%
发文量
0
审稿时长
10 weeks
期刊介绍: Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.
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