| 一类偏序线性代数上的Freudenthal谱定理 |
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| 引用本文： | 辛巧,穆春来.一类偏序线性代数上的Freudenthal谱定理[J].西南农业大学学报,2018,40(12):105-111. |
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| 作者姓名： | 辛巧 穆春来 |
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| 作者单位： | 1. 伊犁师范学院 数学与统计学院, 新疆 伊宁 835000;2. 重庆大学 数学与统计学院, 重庆 401331 |
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| 基金项目： | 新疆维吾尔自治区高等学校科研计划项目（XJEDU2014S064）. |
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| 摘 要： | 利用一类特殊的偏序线性代数上的极大投影的概念,讨论了其上的Freudenthal谱定理,不同于以往的方法,仅仅使用了偏序和Dedekindσ完备的基本概念.最后,给出了一个偏序线性代数的例子,它不是格,但是Freudenthal谱定理依然成立.
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| 关 键 词： | 偏序线性代数 极大和极小投影 Freudenthal谱定理 |
| 收稿时间： | 2017/11/26 0:00:00 |
Freudenthal Spectral Theorem on a Special Class of Partially Ordered Linear Algebra |
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| XIN Qiao,MU Chun-lai.Freudenthal Spectral Theorem on a Special Class of Partially Ordered Linear Algebra[J].Journal of Southwest Agricultural University,2018,40(12):105-111. |
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| Authors: | XIN Qiao MU Chun-lai |
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| Institution: | 1. College of Mathematics and Statistics, Yili Normal University, Yili Xinjiang 835000, China;2. School of Mathematics and Statistics, Chongqing University, Chongqing 401331, China |
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| Abstract: | Using the conception of the maximal projection of the special class of partially ordered linear algebras, we prove the spectral theorem on the partially ordered linear algebras. Specially, only rudimentary concepts such as partial ordering, Dedekind σ completeness are used in this work. Finally, we propose one partially ordered linear algebra, which is not a lattice, but the Freudenthal spectral theorem still holds. |
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| Keywords: | partially ordered linear algebra maximal and minimal projections Freudenthal spectral theorem |
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