A characterisation of Lie algebras using ideals and subalgebras

被引：0
|
作者：
Dotsenko, Vladimir [1 ]
Garcia-Martinez, Xabier [2 ,3 ,4 ,5 ]
机构：
[1] Univ Strasbourg, CNRS, Inst Rech Math Avancee, UMR 7501, Strasbourg, France
[2] Univ Vigo, Esc Sup Enx Informat, Dept Matemat, CITMAga, Campus Ourense, Orense, Spain
[3] Univ Vigo, Orense, Spain
[4] Univ Vigo, CITMAga, Campus Ourense, E-32004 Orense, Spain
[5] Univ Vigo, Dept Matemat, Esc Sup Enx Informat, Campus Ourense, E-32004 Orense, Spain
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2024年 / 56卷 / 07期
关键词：
RADICAL PROPERTIES; EXPONENTIATION; VARIETIES; RINGS;
D O I：
10.1112/blms.13062
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that if, for a non-trivial variety of non-associative algebras, every subalgebra of every free algebra is free and I2$I<^>2$ is an ideal whenever I$I$ is an ideal, then this variety coincides with the variety of all Lie algebras.
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页码：2408 / 2423
页数：16
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