A Note on Rhotrices Ring
Abstract
In this paper, we define algebraic operations on 3-dimensional rhotrices over an arbitrary ring R and show that the set of 3-dimensional rhotrices over an arbitrary ring R is a ring according to these operations. We investigate the properties of a rhotrices ring. Furthermore, we characterize the ideals of a rhotrices ring. Also, maximal ideals and prime ideals of a rhotrices ring are investigated. An example of these concepts is presented.
Keywords
Rhotrix,rhotrices ring,ideals of a rhotrices ring
Project Number
17-223
References
- K. T. Atanassov, A. G. Shannon, Matrix-tertions and Matrix-noitrets: Exercises in Mathematical Enrichment, International Journal of Mathematical Education in Science and Technology 29 (1998) 898-903.
- A. O. Ajibade, The Concept of Rhotrix in Mathematical Enrichment, International Journal of Mathematical Education in Science and Technology 34 (2003) 175-179.
- A. Mohammed, A Remark on The Classifications of Rhotrices as Abstract Structures, International Journal of Physical Sciences 4 (2009) 496-499.
- B. Sani, An Alternative Method for Multiplication of Rhotrices, International Journal of Mathematical Education in Science and Technology 35 (2004) 777-781.
- A. Mohammed, M. Balarabe, First Review of Articles on Rhotrix Theory Since Its Inception, Advances in Linear Algebra and Matrix Theory 4 (2014) 216-224.
- A. Mohammed, The Non-Commutative Full Rhotrix Ring and Its Subring, Science World Journal 13 (2018) 24-36.
- G. Abrams, P. Ara, M. S. Molina, The Leavitt Path Algebra of a Graph, Lecture Notes in Mathematics 2191, Springer, 2017.