Some properties of Camina and $n$-Baer Lie algebras
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 C...
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Shahid Bahonar University of Kerman
2024-12-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4485_ee2c6e4417c7cc259648988ae7b65809.pdf |
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| author | Maryam Ghezelsoflo Mohammad Reza Moghaddam Mohammad Amin Rostamyari Somayeh Saffarnia |
| author_facet | Maryam Ghezelsoflo Mohammad Reza Moghaddam Mohammad Amin Rostamyari Somayeh Saffarnia |
| author_sort | Maryam Ghezelsoflo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d8511046f9d8482a883aa3279fb94a0e |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-d8511046f9d8482a883aa3279fb94a0e2025-01-04T19:29:49ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052024-12-0113415316410.22103/jmmr.2024.23435.16484485Some properties of Camina and $n$-Baer Lie algebrasMaryam Ghezelsoflo0Mohammad Reza Moghaddam1Mohammad Amin Rostamyari2Somayeh Saffarnia3Department of Mathematics, Mashhad Branch Islamic Azad University, Mashhad, IranDepartment of Mathematics, Khayyam University, Mashhad, IranDepartment of Mathematics, Khayyam University, Mashhad, IranDepartment of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, IranLet $I$ 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.https://jmmrc.uk.ac.ir/article_4485_ee2c6e4417c7cc259648988ae7b65809.pdfcamina lie algebra$n$-baer lie algebra$2$-subideal subalgebranilpotent lie algebra |
| spellingShingle | Maryam Ghezelsoflo Mohammad Reza Moghaddam Mohammad Amin Rostamyari Somayeh Saffarnia Some properties of Camina and $n$-Baer Lie algebras Journal of Mahani Mathematical Research camina lie algebra $n$-baer lie algebra $2$-subideal subalgebra nilpotent lie algebra |
| title | Some properties of Camina and $n$-Baer Lie algebras |
| title_full | Some properties of Camina and $n$-Baer Lie algebras |
| title_fullStr | Some properties of Camina and $n$-Baer Lie algebras |
| title_full_unstemmed | Some properties of Camina and $n$-Baer Lie algebras |
| title_short | Some properties of Camina and $n$-Baer Lie algebras |
| title_sort | some properties of camina and n baer lie algebras |
| topic | camina lie algebra $n$-baer lie algebra $2$-subideal subalgebra nilpotent lie algebra |
| url | https://jmmrc.uk.ac.ir/article_4485_ee2c6e4417c7cc259648988ae7b65809.pdf |
| work_keys_str_mv | AT maryamghezelsoflo somepropertiesofcaminaandnbaerliealgebras AT mohammadrezamoghaddam somepropertiesofcaminaandnbaerliealgebras AT mohammadaminrostamyari somepropertiesofcaminaandnbaerliealgebras AT somayehsaffarnia somepropertiesofcaminaandnbaerliealgebras |