English Dictionary

field extension

名詞

(algebra, field theory, algebraic geometry) Any pair of fields, denoted L/K, such that K is a subfield of L.

日本語の意味

体の拡大：代数学、体論、代数幾何学の文脈において、ある体Kを部分体として含む体Lとの組（L/K）を指す概念。

Let L/K be a finite field extension; then the degree [L:K] equals the dimension of L as a vector space over K.

L/Kを有限体拡大とすると、次数[L:K]はK上のベクトル空間としてのLの次元に等しい。

意味（1）

(algebra, field theory, algebraic geometry) Any pair of fields, denoted L/K, such that K is a subfield of L.

A Galois field extension may be defined in terms of its Galois group (Section 2) or in terms of the internal structure of the extension (Section 3).

field extensions （ plural ）