Graded identities for matrix algebras of order two over a finite field
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.
Authors
- Diogo Diniz (ORCID: https://orcid.org/0000-0002-7475-7538)
- Luis Filipe Ramos (ORCID: https://orcid.org/0000-0003-2654-3989)
- Eduardo Pinto da Fonsêca
Publication Details
- Journal
- Communications in Mathematics
- Published
- 2026-10-06
- DOI
- https://doi.org/10.46298/cm.18621
- Primary Topic
- Advanced Topics in Algebra
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico