A note on complete evolution algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909960214937600 |
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| author | García-Martínez, Xabier Pérez-Rodríguez, Andrés |
| author_facet | García-Martínez, Xabier Pérez-Rodríguez, Andrés |
| contents | This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial system of equations using elementary tools from algebraic geometry. We also obtain new results on subalgebras and idempotents of evolution algebras, and conclude by proposing a conjecture that may characterise solvable evolution algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on complete evolution algebras García-Martínez, Xabier Pérez-Rodríguez, Andrés Rings and Algebras 17D92, 17A60 This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial system of equations using elementary tools from algebraic geometry. We also obtain new results on subalgebras and idempotents of evolution algebras, and conclude by proposing a conjecture that may characterise solvable evolution algebras. |
| title | A note on complete evolution algebras |
| topic | Rings and Algebras 17D92, 17A60 |
| url | https://arxiv.org/abs/2512.12418 |