“Galois correspondence”的概念、定义、习题解题方法及翻译-数学辞典

单词

Galois correspondence

释义

Galois correspondence

Let K denote the splitting field of a polynomial f(x) over ℚ and let G denote the Galois group of K: ℚ. Then the degree of K: ℚ equals the order of G. Further for every subgroup H of G we can define its fixed field

which is a subfield of K. And for every subfield F of K,

is a subgroup of G. Then and † are inverses of one another. Further N is a normal subgroup of G if and only if N† is the splitting field of some polynomial. (With further technical additions the correspondence can be extended to base fields other than ℚ.)

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