L-algebras and their ideals: from simplicity to semidirect products
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918239641010176 |
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| author | Properzi, Silvia Qin, Yufei |
| author_facet | Properzi, Silvia Qin, Yufei |
| contents | In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime spectrum. Furthermore, we introduce a family of finite simple L-algebras and prove that every simple linear L-algebra belongs to this family. We also show that the family we construct coincides with the class of simple algebras in a certain subclass of finite CKL-algebras. As an application, we use these results to give a clear description of linear Hilbert algebras and their symmetric semidirect products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | L-algebras and their ideals: from simplicity to semidirect products Properzi, Silvia Qin, Yufei Rings and Algebras Combinatorics Logic Quantum Algebra 03G25, 06D20 In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime spectrum. Furthermore, we introduce a family of finite simple L-algebras and prove that every simple linear L-algebra belongs to this family. We also show that the family we construct coincides with the class of simple algebras in a certain subclass of finite CKL-algebras. As an application, we use these results to give a clear description of linear Hilbert algebras and their symmetric semidirect products. |
| title | L-algebras and their ideals: from simplicity to semidirect products |
| topic | Rings and Algebras Combinatorics Logic Quantum Algebra 03G25, 06D20 |
| url | https://arxiv.org/abs/2512.08579 |