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

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.