| 实封闭域上的代数 |
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| 引用本文： | 徐忠明. 实封闭域上的代数[J]. 浙江理工大学学报, 2011, 0(5) |
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| 作者姓名： | 徐忠明 |
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| 作者单位： | 浙江理工大学理学院; |
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| 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F2n中有子代数同构于C,全阵代数F4n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((-1)～(1/2));(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Fn、Cn与Hn中之一,④若A是中心单代数,则A同构于全阵代数Fn或Hn,⑤若A没有非零幂零理想,则A=sum Mni from i=1 to l,其中Mni∈{Fni,Cni,Hni},i=1,2,…,l。
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| 关 键 词： | 实封闭域 全阵代数 可除代数 复元素域 四元素体 |
Algebras over Real Closed Field |
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| XU Zhong-ming. Algebras over Real Closed Field[J]. Journal of Zhejiang Sci-tech University, 2011, 0(5) |
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| Authors: | XU Zhong-ming |
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| Affiliation: | XU Zhong-ming (Zhejiang Sci-Tech University,Hangzhou 310018,China) |
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| Abstract: | The author constructs complex element field and quartic element division ring over the real closed filed.The following results are obtained: 1.Let F be a field,then(1) there is a subalgebras in the total matrix algebra F2n which is isomorphic to the complex element field C over F(C=F(i)),(2) there is a subalgebras in the total matrix algebra F4n which is isomorphic to the quartic element division ring H over F(H=F(1,i,j,k)).2.The only algebraic extension division rings over the real closed field F are(1) F,... |
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| Keywords: | real closed field total matrix algebra division algebra complex element field quartic element division ring |
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