关于一类Eisenstein数域

数学季刊 ›› 2004, Vol. 19 ›› Issue (4): 368-372.

关于一类Eisenstein数域

College of Science, Southwest University of Science and Technology, Mianyang 621002, China

收稿日期:2002-12-24 出版日期:2004-12-30 发布日期:2024-03-04
作者简介:JIANG Jian-jun(1970-),male,native of Mianyang,Sichuan,a lecturer of Southwest University of Science and Technology,engages in applied mathematics.
基金资助:
SupportedbytheYouthTeacherFoundationofSouthwestUniversityofScienceandTechnology(033069)；

On a Class of Number Fields of Eisenstein Type

College of Science, Southwest University of Science and Technology, Mianyang 621002, China

Received:2002-12-24 Online:2004-12-30 Published:2024-03-04
About author:JIANG Jian-jun(1970-),male,native of Mianyang,Sichuan,a lecturer of Southwest University of Science and Technology,engages in applied mathematics.
Supported by:
SupportedbytheYouthTeacherFoundationofSouthwestUniversityofScienceandTechnology(033069)；

摘要/Abstract

摘要：

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 powerfree and p | m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.

关键词: number , field , , of , Eisenstein , type;totally , , ramified;prime , ideal , , factorization, element of Eisenstein type;subfield of degree p

Abstract: 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 powerfree and p | m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.

Key words: number , field , , of , Eisenstein , type;totally , , ramified;prime , ideal , , factorization, element of Eisenstein type;subfield of degree p

中图分类号:

O156

蒋剑军. 关于一类Eisenstein数域[J]. 数学季刊, 2004, 19(4): 368-372.

JIANG Jian-jun. On a Class of Number Fields of Eisenstein Type[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(4): 368-372.

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