|本期目录/Table of Contents|

[1]徐忠明. 实封闭域上的代数[J].浙江理工大学学报,2011,28(05):814-818.
 XU Zhong ming. Algebras over Real Closed Field[J].Journal of Zhejiang Sci-Tech University,2011,28(05):814-818.
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 实封闭域上的代数()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第28卷
期数:
2011年05期
页码:
814-818
栏目:
生物与生命科学
出版日期:
2011-10-30

文章信息/Info

Title:
 Algebras over Real Closed Field
文章编号:
16733851 (2011) 05081405
作者:
 徐忠明
 浙江理工大学理学院, 杭州 310018
Author(s):
 XU Zhongming
 Zhejiang SciTech University, Hangzhou 310018, China
关键词:
 实封闭域 全阵代数 可除代数 复元素域 四元素体
分类号:
O153.3
文献标志码:
A
摘要:
    在建立了实封闭域F上复元素域C与四元素体H后得到了:(1)全阵代数F2n中有子代数同构于C,全阵代数F4n中有子代数同构于H;(2)F上代数扩张体只有F、C和H;(3)设F是域K里上维数有限的真子域,则F是实封闭的K是代数闭域且K=F(〖KF(〗-1〖KF)〗);(4)设A是F上的有限维代数,①若A是可除代数,则A同构于F、C或H,②若A是中心可除代数,则A同构于F或H,③若A是单代数,则A同构于全阵代数Fn、Cn与Hn中之一,④若A是中心单代数,则A同构于全阵代数Fn或Hn,⑤若A没有非零幂零理想,则A=∑〖DD(〗l〖〗i=1〖DD)〗⊕Mni,其中Mni∈{Fni,Cni,Hni},i=1,2,…,l。

参考文献/References:

[1] Jacobson N. Basic Algebra: Ⅱ[M]. San Francisco: W. H. Freeman and company, 1980: 630657.
[2] 刘绍学, 郭径云, 朱彬, 等. 环与代数[M]. 北京: 科学出版社, 2009: 1379.
[3] 谢邦杰. 抽象代数[M]. 上海: 上海科学技术出版社, 1982: 278357.
[4] Faith C. Algebra I: Rings, Modules, and Categories[M]. New York: SpringerVerlag Berlin Heidelberg, 1981: 461466.
[5] 华罗庚, 万哲先. 华罗庚文集: 代数卷Ⅰ[M]. 北京: 科学技术出版社, 2010: 110.
[6] Shafarevich I R. Notions of Algebra[M]. New York: SpringerVerlag Beidelberg, 2005: 6195.

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备注/Memo

备注/Memo:
 收稿日期: 2010-07-06
作者简介: 徐忠明(1936-),男,浙江新昌人,大学本科,副教授,主要从事代数的研究。
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