COMPUTING SUBFIELDS IN ALGEBRAIC NUMBER-FIELDS

被引:16
|
作者
DIXON, JD
机构
[1] Department of Mathematics and Statistics, Carleton University
关键词
D O I
10.1017/S1446788700032432
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let K : = Q-(alpha) be an algebraic number field which is given by specifying the minimal polynomial f(X) for alpha over Q. We describe a procedure for finding the subfields L of K by constructing pairs (w(X), g(X)) of polynomials over Q such that L = Q(w(alpha)) and g(X) is the minimal polynomial for w(alpha). The construction uses local information obtained from the Frobenius-Chebotarev theorem about the Galois group Gal(f), and computations over p-adic extensions of Q.
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页码:434 / 448
页数:15
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