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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 Downloads: 174586 Total View: 1978859
Frequency: quarterly ISSN Print: 2576-0645 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2024.03.001

Some Results on Heart-oriented Paraletrix Ring

R. U. Ndubuisi1,*, R. B. Abubakar2, O. G. Udoaka3

1Department of Mathematics, Federal University of Technology, Owerri, Nigeria.

2Department of Mathematics, Federal College of Education (T), Omoku, Nigeria.

3Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Nigeria.

*Corresponding author:R. U. Ndubuisi

Published: April 22,2024

Abstract

It is known that rhotrices are objects which are in some ways between (2×2)-dimensional and (3×3)-dimensional matrices. In the literature, several results exist on rhotrices and subsequent studies on the said objects gave rise to another algebraic structure known as paraletrix which this time happens to be the arrangement of objects in the form of a parallelogram. This paper presents some results associated with the heart-oriented paraletrix ring otherwise known as the commutative paraletrix ring in light of known results on rhotrix ring. In particular, we employ the commutative rhotrix approach otherwise known as the heart-oriented rhotrix approach to show that an operation of the integral calculus holds for a heart-oriented paraletrix ring. Consequently, the analogue of Cayley’s theorem and that of arithmetic series in terms of a heart-oriented paraletrix ring are presented. The results obtained in this paper contribute to the already existing works in the literature on paraletrix ring.

References

[1] Aminu, A and Michael, O. (2014). An introduction to the concept of paraletrix, a generalization of rhotrix. AfrikaMatematica, DOI: 10.1007/s13370-014-0251-1.

[2] Ajibade, A.O. (2003). The concept of Rhotrix in mathematical enrichment. International Journal of Mathematical Education in sci-ence and Technology, 34, 175-179.

[3] Sani, B. (2004). An alternative method for multiplication of rhotrices. International Journal of Mathematical Education in Science and Technology, 35, 777-781.

[4] Michael, O and Aminu, A. (2015). The exponential paraletrix. Journal of the Nigerian Association of Mathematical Physics, Vol. 31, pp. 271-278.

[5] Ndubuisi, R. U, Abubakar, R. B, Udoaka, O. G., and Ugbene, I. J. (2021). Characterisation of a heart-oriented paraletrix. Journal of Mathematical and Computational Science, 11(3), 3130-3150.

[6] Ndubuisi, R.U, Nwajeri, U.K., Onyenegecha, C.P, Patil, K.M, Udoaka, O.G., and Osuji, W.I. (2022). Linear mappings in paraletrix spaces and its application to fractional calculus. Notes on Number Theory and Discrete Mathematics, 28(4), 698-709.

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[8] Mohammed, A. A. (2007). Note on rhotrix exponential rule and its applications to special series and polynomial equations defined over rhotrices. Notes on Number Theory and Discrete Maths, 13, 1-15.

How to cite this paper

Some Results on Heart-oriented Paraletrix Ring

How to cite this paper: R. U. Ndubuisi, R. B. Abubakar, O. G. Udoaka. (2024) Some Results on Heart-oriented Paraletrix RingJournal of Applied Mathematics and Computation, 8(1), 1-6.

DOI: http://dx.doi.org/10.26855/jamc.2024.03.001