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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.00981 |
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| _version_ | 1866910393737150464 |
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| author | Abdurasulov, K. Adashev, J. Normatov, Z. Solijonova, Sh. |
| author_facet | Abdurasulov, K. Adashev, J. Normatov, Z. Solijonova, Sh. |
| contents | This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum is associative. In particular, the paper is devoted to classifying anti-dendriform algebras associated with null-filiform associative algebras and three-dimensional algebras. It is known that any finite-dimensional associative algebra without a non-zero idempotent element is nilpotent. If an associative algebra has a non-zero idempotent element, then there does not exist a compatible anti-dendriform algebra structure associated with associative algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of three-dimensional anti-dendriform algebras Abdurasulov, K. Adashev, J. Normatov, Z. Solijonova, Sh. Rings and Algebras 16P10, 17A30 This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum is associative. In particular, the paper is devoted to classifying anti-dendriform algebras associated with null-filiform associative algebras and three-dimensional algebras. It is known that any finite-dimensional associative algebra without a non-zero idempotent element is nilpotent. If an associative algebra has a non-zero idempotent element, then there does not exist a compatible anti-dendriform algebra structure associated with associative algebras. |
| title | Classification of three-dimensional anti-dendriform algebras |
| topic | Rings and Algebras 16P10, 17A30 |
| url | https://arxiv.org/abs/2404.00981 |