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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/2405.03531 |
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| _version_ | 1866915082606215168 |
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| author | Alhussein, H. Kolesnikov, P. |
| author_facet | Alhussein, H. Kolesnikov, P. |
| contents | We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional algebras, the nilpotency condition is necessary for a commutative algebra to have a pre-commutative envelope. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the pre-commutative envelopes of commutative algebras Alhussein, H. Kolesnikov, P. Rings and Algebras We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional algebras, the nilpotency condition is necessary for a commutative algebra to have a pre-commutative envelope. |
| title | On the pre-commutative envelopes of commutative algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2405.03531 |