A Complete classification of two-dimensional endo-commutative algebras over an arbitrary field
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910516783349760 |
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| author | Asrorov, D. Bekbaev, U. Rakhimov, I. |
| author_facet | Asrorov, D. Bekbaev, U. Rakhimov, I. |
| contents | In the paper, we consider the class of so-called endo-commutative algebras. From the identity imposed to specify this class, one can easily see that the product in this class preserves the square of elements. We give a complete classification of this class, up to isomorphism, over any basic field in dimension two. This elementary and self-contained exposition uses the recent result of one of the authors on description of the category of all $2$-dimensional algebras over any basic field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00491 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Complete classification of two-dimensional endo-commutative algebras over an arbitrary field Asrorov, D. Bekbaev, U. Rakhimov, I. Rings and Algebras In the paper, we consider the class of so-called endo-commutative algebras. From the identity imposed to specify this class, one can easily see that the product in this class preserves the square of elements. We give a complete classification of this class, up to isomorphism, over any basic field in dimension two. This elementary and self-contained exposition uses the recent result of one of the authors on description of the category of all $2$-dimensional algebras over any basic field. |
| title | A Complete classification of two-dimensional endo-commutative algebras over an arbitrary field |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2304.00491 |