In this paper, we first classify all associative algebra structures on a two-dimensional vector space over an arbitrary base field equipped with a non-degenerate bilinear form. We then determine which of these are Frobenius algebras. We provide lists of canonical representatives of the isomorphism classes of these algebras over an arbitrary base field.
| Mualliflar | Asrorov , D.U., Bekbaev , U.D., Rakhimov , I.S. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-11-03 |
| Jild | 69 |
| Son | 4 |
| Betlar | 22-34 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-4-3 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-4-3 · Maqolaning asl sahifasi
Frobenius algebra, Non-degenerate bilinear form, Classification, Automorphism
| APA | Asrorov , D.U., Bekbaev , U.D., & Rakhimov , I.S. (2025). Classification of Frobenius algebra structures on two-dimensional vector space over any base field. O‘zbekiston matematika jurnali, 69(4), 22-34. https://doi.org/10.29229/uzmj.2025-4-3 |
|---|---|
| GOST (OAK) | Asrorov , D.U., Bekbaev , U.D., Rakhimov , I.S. Classification of Frobenius algebra structures on two-dimensional vector space over any base field // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 22-34. – DOI: 10.29229/uzmj.2025-4-3. |
| MLA | Asrorov , D.U., Bekbaev , U.D., and Rakhimov , I.S. “Classification of Frobenius algebra structures on two-dimensional vector space over any base field.” O‘zbekiston matematika jurnali, 69(4), 22-34, 2025. https://doi.org/10.29229/uzmj.2025-4-3 |
| Chicago | Asrorov , D.U., Bekbaev , U.D., and Rakhimov , I.S. “Classification of Frobenius algebra structures on two-dimensional vector space over any base field.” O‘zbekiston matematika jurnali, 69(4), 22-34 (2025). https://doi.org/10.29229/uzmj.2025-4-3 |
| Harvard | Asrorov , D.U., Bekbaev , U.D., and Rakhimov , I.S (2025) ‘Classification of Frobenius algebra structures on two-dimensional vector space over any base field’, O‘zbekiston matematika jurnali, 69(4), 22-34. https://doi.org/10.29229/uzmj.2025-4-3 |
| BibTeX | @article{asrorovdu2025,
title = {Classification of Frobenius algebra structures on two-dimensional vector space over any base field},
author = {Asrorov , D.U. and Bekbaev , U.D. and Rakhimov , I.S.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {4},
pages = {22-34},
doi = {10.29229/uzmj.2025-4-3},
url = {https://doi.org/10.29229/uzmj.2025-4-3}
} |
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