JP Journal of Algebra, Number Theory and Applications

The JP Journal of Algebra, Number Theory and Applications is a prestigious international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research papers, both theoretical and applied in nature, in various branches of algebra and number theory. The journal also welcomes survey articles that contribute to the advancement of these fields.

Submit Article

CLASSIFICATION AND DERIVATIONS OF FOUR-DIMENSIONAL ALMOST BERNSTEIN ALGEBRAS

Authors

  • Paul Beremwidougou
  • André Conseibo

Keywords:

Peirce decomposition, type of algebra, Bernstein algebra, almost Bernstein algebra, train algebra, idempotent, derivation

DOI:

https://doi.org/10.17654/0972555522022

Abstract

In this paper, we first give some general results specifying the necessary conditions that must be satisfied by an almost Bernstein algebra. In the second step, we proceed to the classification of almost Bernstein algebras of dimension four. Finally, we describe the derivations of an almost Bernstein algebra.

Received: March 4, 2022
Accepted: April 27, 2022

References

R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York, 1966.

P. Holgate, Genetic algebras satisfying Bernstein’s stationarity principle, J. Lond. Math. Soc., II Ser. 9 (1975), 613-623.

M. T. Alcalde, C. Burgueño, A. Labra and A. Micali, Sur les algèbres de Bernstein (On Bernstein algebras), Proc. Lond. Math. Soc. (3) 58(1) (1989), 51 68.

S. Bernstein, Solution of a mathematical problem connected with the theory of heredity, Ann. Math. Stat. 13 (1942), 53-61.

S. Walcher, Bernstein algebras which are Jordan algebras, Arch. Math. 50(3) (1988), 218-222.

J. López-Sánchez and S. M. E. Rodríguez, On train algebras of rank 4, Comm. Algebra 24(14) (1996), 4439-4445.

J. Bayara, A. Conseibo, M. Ouattara and A. Micali, Train algebras of degree 2 and exponent 3, Discrete Contin. Dyn. Syst. Ser. S 4(6) (2011), 1371-1386.

P. Beremwidougou and A. Conseibo, Algebras satisfying identity of almost Bernstein algebras, Far East J. Math. Sci. (FJMS) 131(2) (2021), 131-152.

A. Wörz-Busekros, Algebras in genetics, Lecture Notes in Biomathematics, 36, Springer-Verlag, Berlin, New York, 1980.

Published

2022-07-01

Issue

Section

Articles

How to Cite

CLASSIFICATION AND DERIVATIONS OF FOUR-DIMENSIONAL ALMOST BERNSTEIN ALGEBRAS. (2022). JP Journal of Algebra, Number Theory and Applications, 56, 1-25. https://doi.org/10.17654/0972555522022

Similar Articles

1-10 of 57

You may also start an advanced similarity search for this article.