Varieties of bicommutative algebras with identity of degree three
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913109395898368 |
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| author | Drensky, Vesselin Zhakhayev, Bekzat |
| author_facet | Drensky, Vesselin Zhakhayev, Bekzat |
| contents | The variety of bicommutative algebras is the class of all nonassociative algebras satisfying the polynomial identities $(x_1x_2)x_3=(x_1x_3)x_2$ and $x_1(x_2x_3)=x_2(x_1x_3)$. In this paper we provide a complete description of varieties of bicommutative algebras over a field of characteristic zero that satisfy a polynomial identity of degree three. Furthermore, we establish a sufficient and necessary condition for a variety of bicommutative algebras to have a distributive lattice of subvarieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09512 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Varieties of bicommutative algebras with identity of degree three Drensky, Vesselin Zhakhayev, Bekzat Rings and Algebras 17A30, 17A50, 20C30 The variety of bicommutative algebras is the class of all nonassociative algebras satisfying the polynomial identities $(x_1x_2)x_3=(x_1x_3)x_2$ and $x_1(x_2x_3)=x_2(x_1x_3)$. In this paper we provide a complete description of varieties of bicommutative algebras over a field of characteristic zero that satisfy a polynomial identity of degree three. Furthermore, we establish a sufficient and necessary condition for a variety of bicommutative algebras to have a distributive lattice of subvarieties. |
| title | Varieties of bicommutative algebras with identity of degree three |
| topic | Rings and Algebras 17A30, 17A50, 20C30 |
| url | https://arxiv.org/abs/2605.09512 |