分圆域Q(ζ_(33))的幂元整基  

Power Integral Bases of Cyclotomic FieldQ(ζ33)

作　　者：袁昌斌[1] 

机构地区：[1]马鞍山职业技术学院,安徽马鞍山243011

出　　处：《大学数学》2010年第3期103-107,共5页College Mathematics

摘　　要：伽罗华数域L称有一个幂元整基,如果其代数整数环具有形式Ζα,其中α∈L.此时称α是L的幂元整基生成元.设α,β是L的两个幂元整基生成元,若β=m±σ(α),m∈Z,σ∈Gal(L/Q),则称α与β等价.本文主要研究分圆域Q(ζ33)的幂元整基问题.分圆域Q(ζ33)的代数整环是Z[ζ33],所以ζ33是Q(ζ33)的幂元整基生成元.设α是Q(ζ33)的幂元整基生成元,证明了当α+ā■Z时,α与ζ33等价.从而给出在此条件下分圆域Q(ζ33)的所有幂元整基生成元.A galois number field L is said to have a power bases if its ring of integers is of the form Z[α] for some α∈L.In this case α is called a generator of power bases in L.Let α and β be generators of two power bases in L,α and β is called equivalent if β=m±σ（α） for some m∈Z,σ∈Gal（L/Q）.In this paper,we discuss the generators of power integral bases of cycloyomic field Q（ζ33）.Z[ζ33]is the ring of integers of the cycloyomic field Q（ζ33）,so ζ33 generates a power integral bases for Q（ζ33）.Let α be another generator of a power integral bases of cyclotomic Q（ζ33）,We proved that if α＋ā Z,then α is equivalent to ζ33.Therefore,we can get all the generators of power integral bases for the cyclotomic field Q（ζ33） under the case.

关 键 词：幂元整基 分圆域 生成元 单位 

分 类 号：O156.23[理学—数学]