Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

Submit Article

NOTES ON SOME NONCOMMUTATIVE, NONALTERNATIVE, FLEXIBLE ALGEBRAS

Authors

  • Youngkwon Song

Keywords:

nonassociative commutative quaternions, octonions.

DOI:

https://doi.org/10.17654/0972087125006

Abstract

In this paper, the existence of solutions for some fundamental equations with coefficients in $H^*, M_{n \times n}\left(H^*\right), H_8^*$ and $M_{n \times n}\left(H_8^*\right)$ is investigated.

Received: October 1, 2024
Revised: October 30, 2024
Accepted: November 15, 2024

References

H. Kosal and M. Tosun, Commutative quaternion matrices, Adv. Appl. Clifford. Algebras 24 (2014), 769-779.

A. Pogorui and M. Shapiro, On the structure of the set of zeros of quaternionic polynomials, Complex Var. Theory Appl. 49 (2004), 379-389.

S. Pumplun and S. Walcher, On the zeros of polynomials over quaternions, Comm. Algebra 30 (2002), 4007-4018.

C. Segre, The real representations of complex elements and extension to bicomplex systems, Math. Ann. 40 (1892), 413-467.

R. Serôdio, E. Pereira and J. Vitória, Computing the zeros of quaternionic polynomials, Comput. Math. Appl. 42 (2001), 1229-1237.

Y. Song, Construction of commutative number systems, Linear Multilinear Algebra 70 (2020), 2382-2396.

Y. Song, Matrices of nonassociative commutative quaternions, Far East J. Math. Sci. (FJMS) 137 (2022), 39-52.

Y. Song, Construction of eight dimensional nonalternative, noncommutative algebra, J. Chungcheong Math. Soc. 36(4) (2023), 255-265.

Published

2024-11-26

Issue

Section

Articles

How to Cite

NOTES ON SOME NONCOMMUTATIVE, NONALTERNATIVE, FLEXIBLE ALGEBRAS. (2024). Far East Journal of Mathematical Sciences (FJMS), 142(1), 71-84. https://doi.org/10.17654/0972087125006