Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CLASSIFICATION OF FOUR DIMENSIONAL BARIC ALGEBRAS SATISFYING POLYNOMIAL IDENTITY OF DEGREE SIX

  • Kabre Daouda (Departement de mathematiques, Universite Norbert ZONGO) ;
  • Dembega Abdoulaye (Departement de mathematiques, Universite Norbert ZONGO) ;
  • Conseibo Andre (Departement de mathematiques, Universite Norbert ZONGO)
  • Received : 2023.11.25
  • Accepted : 2024.03.07
  • Published : 2024.03.30
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Abstract

In this paper, we proceeded to the classification of four dimensional baric algebras strictly satisfying a polynomial identity of degree six. After some results on the structure of such algebras, we show that the type of an algebra of the studied class is an invariant under change of idempotent in the Peirce decomposition. This last result plays a major role in our classification.

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References

  1. J.Bayara, A. Conseibo, Ouattara, M. and A.Micali, Train algebras of degree 2 and exponent 3, Discret and continous dynamical systems series, 4 (6), (2011), 1371-1386. https://doi.org/10.3934/dcdss.2011.4.1371 
  2. P.Beremwidougou, and A.Conseibo, Algebras satisfying identity of almost Bernstein algebras, Far East J. Math. Sci. (FJMS) 131 (2) (2021), 131-152. https://doi.org/10.17654/ms131020131 
  3. S. N.Bernstein, Demonstration mathematique de la loi d'heredite de Mendel, C. R. Acad. Sci. Paris, 177, (1923), 528-531. 
  4. S. N.Bernstein, Principe de stationnarite et generalisation de la loi de Mendel, C. R. Acad. Sci. Paris, 177, (1923), 581-584. 
  5. I. M. H. Etherington, Genetic algebras, Proceedings of the Royal Society of Edinburgh, 59 (1939), 242-258. 
  6. B. L. M.Ferreira, H.Guzzo, J. C. M.Ferreira, The Wedderburn b-decomposition for a class of almost alternative baric algebras, Asian-European Journal of Mathematics, 08 (2015), p. 1550006. https://doi.org/10.1142/S1793557115500060 
  7. B. L. M.Ferreira, R. N.Ferreira, The Wedderburn b-decomposition for Alternative Baric Algebras, Mitt. Math. Ges. Hamburg, 37 (2017), 13-25. https://doi.org/10.48550/arXiv.1410.7078 
  8. B. L. M.Ferreira, The b-radical of generalized alternative balgebras II, PROYECCIONES JOURNAL OF MATHEMATICS, 38 (2019), 969-979. https://doi.org/10.22199/issn.0717-6279-2019-05-0062 
  9. Ph.Holgate, Genetic algebras satisfying Bernstein's stationarity principle, J. London Math. Soc., 2 (9) (1975), 613-623. https://doi.org/10.1112/jlms/s2-9.4.613 
  10. D. Kabre and A. Conseibo, Structure of baric algebras satisfying a polynomial identity of degree six, JP Journal of Algebra Number Theory and Applications, 61 (1), (2023), 37-52. http://dx.doi.org/10.17654/0972555523010 
  11. D. Kabre and A. Conseibo, Algebras satisfying a polynomial identity of degree six that are principal train, European Journal of Pure and Applied Mathematics, 16 (3), (2023), 1480-1490. https://doi.org/10.29020/nybg.ejpam.v16i3.4787 
  12. C. Mallol and al., On the train algebras of degree four: structures and classifications, Commun. Algebra 37(2), (2009) 532-547 . http://dx.doi.org/10.1080/00927870802251146 
  13. M. Nourigat and R. Varro, Study of commutative ω-PI algebras of degree 4. III: Barycentric invariant algebras by gametization, Commun. Algebra 41 (8), (2013), 2825-2851. https://doi.org/10.1080/00927872.2012.665532 
  14. R. D.Schafer, Structure of genetic algebras, Amer. J. Math., 71 (1949), 121-135. https://doi.org/10.2307/2372100 
  15. R.Varro, Multilinear identities of degree 4 for Bernstein algebra and noncommutative mutation algebras, Commun. Algebra 40 (7), (2012), 2426-2448. https://doi.org/10.1080/00927872.2011.578605 
  16. A. Worz-Busekros, Algebras in Genetics, Lecture Notes in Biomathematics, 36, Springer-Verlag, Berlin-New York, 1980.