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单词 Fundamental theorem of Galois theory
释义

Fundamental theorem of Galois theory

中文百科

伽罗瓦理论基本定理

子群与子域的关联结构图
子群与子域的关联结构图
Lattice of subgroups and subfields
Lattice of subgroups and subfields

伽罗瓦理论基本定理是抽象代数中的定理,通过群的概念来描述特定域扩张的细致结构。定理说明了,如果某个域扩张L/K是有限伽罗瓦扩张,则此扩张的伽罗瓦群的子群与其中间域(即子扩张KFL中的F)之间有一一对应关系。

英语百科

Fundamental theorem of Galois theory 伽罗瓦理论基本定理

Lattice of subgroups and subfields
Lattice of subgroups and subfields
子群与子域的关联结构图
子群与子域的关联结构图

In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions.

In its most basic form, the theorem asserts that given a field extension E/F that is finite and Galois, there is a one-to-one correspondence between its intermediate fields and subgroups of its Galois group. (Intermediate fields are fields K satisfying FKE; they are also called subextensions of E/F.)

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更新时间:2025/6/19 21:49:30