| 释义 |
Galois|galwa|
The name of É. Galois (1811–32), French mathematician, used attrib. to designate various concepts in algebra arising out of his work, as Galois field, a field with a finite number of elements; Galois function, Galois group, Galois resolvent, Galois theory. So Gaˈloisian a.
1893E. H. Moore in Bull. N.Y. Math. Soc. III. 75 The Galois-field of order s = qn, GF[qn], consists of the system of qn incongruous classes (modulis q, Fn(ξ)) of rational integral functions of ξ with integral coefficients. Ibid., Galois theory. 1898Bull. Amer. Math. Soc. IV. 335 This is precisely the Galoisian scheme of solution. 1899Ibid. V. 237 Galois group. 1900J. Pierpont in Ann. Math. 2nd Ser. I. 124 Any one of the equations Gk(t) = 0 is called a Galoisian Resolvent of (A) for R. Ibid. 125 We shall for convenience of notation take G1 = 0. We shall call this the Galoisian Resolvent. 1901Burnside & Panton Theory of Equations (ed. 4) II. xx. 246 This function, ψ1, is called the Galois Function. Ibid. 257 The equation of the Nth degree whose roots are these N values, viz., Ψ(z)≡(z - ψ1)(z - ψ2)..(z - ψn) = 0, is called the Galois resolvent. 1937R. D. Carmichael Introd. Groups of Finite Order ix. 255 A particular Galois field, so far as its abstract properties are concerned, is completely determined by its order. 1963G. D. Mostow et al. Fund. Struct. Algebra x. 297 Galois theory shows that the roots of the polynomial can be obtained from the coefficients ai by ordinary field operations (+, -, ×, {div}) and root extractions if and only if the Galois group is solvable. 1965Patterson & Rutherford Elem. Abstract Algebra iii. 97 It can be shown that for each prime number p and each positive integer n, there is essentially only one field consisting of pn elements; this..is called a Galois field. |