On central characteristic ideals and quasi-Noetherian Leibniz algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913184238010368 |
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| author | Bogmis, Narcisse G. Bell Tcheka, Calvin Biyogmam, Guy R. |
| author_facet | Bogmis, Narcisse G. Bell Tcheka, Calvin Biyogmam, Guy R. |
| contents | In this paper, we define on one hand, the notions of characteristics as well as central characteristics ideals of a given Leibniz algebra g and provide a necessary condition under which for two given subalgebras J and K of g such that, J IS a a non empty subset of K. J is a central characteristics two-sided ideal of K. On the other hand, we introduce the class of quasi-Noetherian Leibniz algebras. This generalizes both the class of Noetherian Leibniz algebras and that of quasi-Noetherian Lie algebras introduced by Falih and Stewart. We provide a necessary condition for a Leibniz algebra to be quasi-Noetherian. As in the case of Lie algebras, quasi-Noetherian Leibniz algebras are shown to be closed under quotients, but not under extensions. Finally, we leverage the maximal condition of abelian ideals to provide a characterization of Noetherian Leibniz algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01378 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On central characteristic ideals and quasi-Noetherian Leibniz algebras Bogmis, Narcisse G. Bell Tcheka, Calvin Biyogmam, Guy R. Rings and Algebras 17A32, 17B55, 18B99 In this paper, we define on one hand, the notions of characteristics as well as central characteristics ideals of a given Leibniz algebra g and provide a necessary condition under which for two given subalgebras J and K of g such that, J IS a a non empty subset of K. J is a central characteristics two-sided ideal of K. On the other hand, we introduce the class of quasi-Noetherian Leibniz algebras. This generalizes both the class of Noetherian Leibniz algebras and that of quasi-Noetherian Lie algebras introduced by Falih and Stewart. We provide a necessary condition for a Leibniz algebra to be quasi-Noetherian. As in the case of Lie algebras, quasi-Noetherian Leibniz algebras are shown to be closed under quotients, but not under extensions. Finally, we leverage the maximal condition of abelian ideals to provide a characterization of Noetherian Leibniz algebras. |
| title | On central characteristic ideals and quasi-Noetherian Leibniz algebras |
| topic | Rings and Algebras 17A32, 17B55, 18B99 |
| url | https://arxiv.org/abs/2401.01378 |