李Rinehart代数的子代数若干性质

王雪冰, 牛艳君, 陈良云

数学学报 ›› 2019, Vol. 62 ›› Issue (3) : 353-360.

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PDF(374 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (3) : 353-360. DOI: 10.12386/A2019sxxb0033
论文

李Rinehart代数的子代数若干性质

    王雪冰1, 牛艳君2, 陈良云3
作者信息 +

Some Properties of Subalgebras of Lie-Rinehart Algebras

    Xue Bing WANG1, Yan Jun NIU2, Liang Yun CHEN3
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文章历史 +

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.

Abstract

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-Rinehart 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

Key words

Lie-Rinehart algebras / c-supplemented Lie-Rinehart algebras / E-Lie-Rinehart algebras / Frattini subalgebras

引用本文

导出引用
王雪冰, 牛艳君, 陈良云. 李Rinehart代数的子代数若干性质. 数学学报, 2019, 62(3): 353-360 https://doi.org/10.12386/A2019sxxb0033
Xue Bing WANG, Yan Jun NIU, Liang Yun CHEN. Some Properties of Subalgebras of Lie-Rinehart Algebras. Acta Mathematica Sinica, Chinese Series, 2019, 62(3): 353-360 https://doi.org/10.12386/A2019sxxb0033

参考文献

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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)及吉林省教育厅项目(JJKH20180005K)

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