一类偏序线性代数上的Freudenthal谱定理  

Freudenthal Spectral Theorem on a Special Class of Partially Ordered Linear Algebra

作　　者：辛巧[1] 穆春来[2] XIN Qiao;MU Chun-lai(College of Mathematics and Statistics,Yili Normal University,Yili Xinjiang 835000,China;School of Mathema tics and Sta tistics,Chongqing University,Chongqing 401331,China)

机构地区：[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

出　　处：《西南大学学报（自然科学版）》2018年第12期105-111,共7页Journal of Southwest University(Natural Science Edition)

基　　金：新疆维吾尔自治区高等学校科研计划项目(XJEDU2014S064)

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.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,Dedekindσcompleteness 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.

关 键 词：偏序线性代数 极大和极小投影 Freudenthal谱定理 

分 类 号：O177.7[理学—数学]