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On the trace identities of 2-dimensional tr-prime algebras over a finite field

  • Lucio Centrone
  • Rosiele Trindade Barbosa
  • Felipe Yasumura
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Abstract

We study associative algebras endowed with a trace map. We classify the two-dimensional trace-prime algebras over an arbitrary field. In addition, when the base field is finite, for each such algebra, we provide a finite basis for the T-ideal of trace polynomial identities.

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Cite

BibTeXRIS
BibTeX
@misc{centrone2026trace,
  title = {{On the trace identities of 2-dimensional tr-prime algebras over a finite field}},
  author = {Lucio Centrone and Rosiele Trindade Barbosa and Felipe Yasumura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19797},
  eprint = {2609.19797},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19797},
}
RIS
TY  - UNPB
TI  - On the trace identities of 2-dimensional tr-prime algebras over a finite field
AU  - Lucio Centrone
AU  - Rosiele Trindade Barbosa
AU  - Felipe Yasumura
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19797
UR  - https://arxiv.org/abs/2609.19797
AB  - We study associative algebras endowed with a trace map. We classify the two-dimensional trace-prime algebras over an arbitrary field. In addition, when the base field is finite, for each such algebra, we provide a finite basis for the T-ideal of trace polynomial identities.
ER  -