| 单词 | field extension |
| 释义 | > as lemmasfield extension field extension n. [after German Körpererweiterung (1904 or earlier)] Mathematics a field of which a given field is a subfield. ΚΠ 1937 Trans. Amer. Math. Soc. 41 255 The equations..have a non-trivial solution (in a suitable extension field of K).] 1945 Trans. Amer. Math. Soc. 57 1 The multiplicity of the origin O in the intersection of two curves f(X, Y) = 0, g(X, Y) = 0 may be defined to be the degree of the field extension K((X, Y))⁄K((f, g)). 1956 Philos. Trans. (Royal Soc.) A. 248 407 In this paper we..discuss the existence of a number of field theoretical algorithms in explicit fields, and the effective construction of field extensions. 2006 F. Lorenz Algebra I. iii. 26 Let E/K be a field extension and suppose α ∈ E is algebraic over K. < as lemmas |
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