李Rinehart代数的子代数若干性质  

Some Properties of Subalgebras of Lie-Rinehart Algebras

作　　者：王雪冰[1] 牛艳君[2] 陈良云[3] Xue Bing WANG;Yan Jun NIU;Liang Yun CHEN(Department of Basic, Songyuan Vocational Technical College, Songyuan 1138001, P. R. China;College of Sciences, Changchun Institute of Technology, Changchun 130024, P. R. China;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China)

机构地区：[1]松原职业技术学院基础部,松原138001 [2]长春工程学院理学院,长春130024 [3]东北师范大学数学与统计学院,长春130024

出　　处：《数学学报（中文版）》2019年第3期353-360,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11771069);吉林省自然科学基金资助项目(20170101048JC);吉林省教育厅项目(JJKH20180C05K)

摘　　要：本文主要把李代数的c-可补、E-代数的性质以及Frattini理论推广到更为广泛的李Rinehart代数,得到它们的若干性质,给出了可解李Rinehart代数的一个必要条件.同时,分别获得判断c-可补李Rinehart代数和E-李Rinehart代数的一个充分必要条件.We develop c-supplemented subalgebras, E-algebras and Frattini theory of Lie algebras for Lie-Rinehart algebras, obtain its some important properties and give a necessary conditions for solvable Lie-Rinehaxt algebras. Moreover, we obtain a necessary and sufficient conditions for E-Lie-Rinehart algebras and c-supplemented Lie-Rinehart algebras, respectively.

关 键 词：李Rinehart代数 c-可补李Rinehart代数 E-李Rinehart代数 FRATTINI子代数 

分 类 号：O152.5[理学—数学]