Some properties of Camina and $n$-Baer Lie algebras

Document Type : Special Issue Dedicated to Prof. Esfandiar Eslami

Authors

1 Department of Mathematics, Mashhad Branch Islamic Azad University, Mashhad, Iran

2 Department of Mathematics, Khayyam University, Mashhad, Iran

3 Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

Let $I$ be a non-zero proper ideal of a Lie algebra $L$. Then $(L, I)$ is called a Camina pair if $I \subseteq [x,L]$, for all $x \in L\setminus I$. Also, $L$ is called a Camina Lie algebra if $(L, L^2)$ is a Camina pair. We first give some properties of Camina Lie algebras, and then show that all Camina Lie algebras are soluble. Also, a new notion of $n$-Baer Lie algebras is introduced, and we investigate some of its properties, for $n=1, 2$. A Lie algebra $L$ is said to be $2$-Baer if for any one dimensional subalgebra $K$ of $L$, there exists an ideal $I$ of $L$ such that $K$ is an ideal of $I$. Finally, we study three classes of Lie algebras with $2$-subideal subalgebras and give some relations among them.

Keywords

Main Subjects

References

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Journal of Mahani Mathematical Research
Volume 13, Issue 4 - Serial Number 29
Special issue dedicated to Professor Esfandiar Eslami
December 2024
Pages 153-164

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History

  • Receive Date: 14 May 2024
  • Revise Date: 21 June 2024
  • Accept Date: 18 October 2024

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