In this paper the author determine the factorization of p and the number of p-th subfields of the splitting field K of the irreducible binomial x^p-m(m is p-th powerfreeand p|m) and obtain that all p-th subfields of K...In this paper the author determine the factorization of p and the number of p-th subfields of the splitting field K of the irreducible binomial x^p-m(m is p-th powerfreeand p|m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.展开更多
文摘In this paper the author determine the factorization of p and the number of p-th subfields of the splitting field K of the irreducible binomial x^p-m(m is p-th powerfreeand p|m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.