A Class of Simple Modules for Electrical Lie Algebra of Type D5

The simple modules for electrical Lie algebra of type D₅ were investigated. The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules. The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp₄ or Verma module.     

提高直流系统馈线支路供电可靠性

直流电源作为继电保护、测控、通讯自动化、事故照明、断路器、隔离开关操作机构等设备的工作电源,其供电的可靠性直接关系到变电站的安全稳定运行,因此防止直流系统各馈线支路供电故障就是我们迫切需要解决的问题,对宜昌供电公司220kV变电站直流系统供电方式的现状进行了详细的调查,找出了影响馈线支路供电可靠性的共性问题并提出了最佳的改进方案,使完善后的直流系统简洁清晰,满足直流系统供电的安全、稳定性。     

On Endomorphisms of Normal Orthogroups

As well known, a normal orthogroup is a strong semilattice of rectangular groups. In this paper, we consider the homomorphisms between normal orthogroups and endomorphisms of themselves, relating them to the homomorphisms and endomorphisms of the underlying rect-angular groups with their compositions.     

Lie Bialgebra Structures on Generalized Heisenberg-Virasoro Algebra

In a recent article by Liu,Pei,and Zhu,Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra were determined. By disposing the indexing set, the generalized Heisenberg-Virasoro algebra was considered. It is proved that all Lie bialgebra structures on centerless generalized Heisenberg-Virasoro algebra L are coboundary triangular by proving that the first cohomology group H1 （L,V） =0.     

Jacobson-Bourbaki Correspondence Theorem for Noncommutative Rings

In algebra, the Jacobson-Bourbaki theorem is especially useful for generalizations of the Galois theory of finite, normal and separable field extensions. It was obtained by Jacobson for fields and extended to division rings by Jacobson and Cartan who credited the result to unpublished work by Bourbaki. In 2005, the Jacobson-Bourbaki correspondence theorem for commutative rings was formulated by Winter. And this theorem for augmented rings was formulated by Kadison in 2012. In this paper, we prove the Jacobson-Bourbaki theorem for noncommutative rings which is finitely generated over their centers. We establish a bijective correspondence between the set of subdivisions which are right finite codimension in A and the set of Galois rings of the additive endomorphisms End A of A which is finitely generated over its center.     

π-群强半格的同余

一个半群是Clifford半群当且仅当它是群的强半格，π-群是群在π-正则半群范围内的推广.同余是研究半群性质和结构的重要手段和工具.研究了π-群的强半格上的正则同余，并给出了π-群强半格上的同余是正则同余的充要条件.