Graded identities for matrix algebras of order two over a finite field
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911729477222400 |
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| author | Diniz, Diogo da Fonsêca, Eduardo Pinto Ramos, Luis Filipe |
| author_facet | Diniz, Diogo da Fonsêca, Eduardo Pinto Ramos, Luis Filipe |
| contents | Let $G$ be an arbitrary group and let $\mathbb{F}$ be a finite field. In this paper, we determine bases for the $T_G$-ideals of graded polynomial identities of the algebra $M_2(\mathbb{F})$ for all possible $G$-gradings. The bases obtained consist of finitely many non-trivial graded identities, and are finite whenever $G$ is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30494 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graded identities for matrix algebras of order two over a finite field Diniz, Diogo da Fonsêca, Eduardo Pinto Ramos, Luis Filipe Rings and Algebras 16W50, 16R10 Let $G$ be an arbitrary group and let $\mathbb{F}$ be a finite field. In this paper, we determine bases for the $T_G$-ideals of graded polynomial identities of the algebra $M_2(\mathbb{F})$ for all possible $G$-gradings. The bases obtained consist of finitely many non-trivial graded identities, and are finite whenever $G$ is finite. |
| title | Graded identities for matrix algebras of order two over a finite field |
| topic | Rings and Algebras 16W50, 16R10 |
| url | https://arxiv.org/abs/2605.30494 |