Matrices of the Zero Divisor Graphs of Classes of 3-Radical Zero Completely Primary Finite Rings

Frank Omondi Ndago; Maurice Owino Oduor; Michael Onyango Ojiema

doi:10.51867/scimundi.4.maths.1.1

Authors

Frank Omondi Ndago Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya https://orcid.org/0000-0002-6667-9277
Maurice Owino Oduor Department of Mathematics and Computer Science, University of Kabianga, P.O.Box 2030-20200 Kericho, Kenya
Michael Onyango Ojiema Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100,. Kakamega, Kenya https://orcid.org/0000-0001-9635-7597

DOI:

https://doi.org/10.51867/scimundi.4.maths.1.1

Keywords:

3-Radical Zero Finite Rings, Completely Primary Finite Rings, Zero Divisor Graph

Abstract

The study of finite completely primary rings through the zero divisor graphs, the unit groups and their associated matrices, and the automorphism groups have attracted much attention in the recent past. For the Galois ring R′ and the 2-radical zero finite rings, the mentioned algebraic structures are well understood. Studies on the 3-radical zero finite rings have also been done for the unit groups and the zero divisor graphs Γ(R). However, the characterization of the matrices associated with these graphs has not been exhausted. It is well known that proper understanding of the classification of zero divisor graphs with diameter 2 and girth 3 can provide insights into the structure of commutative rings and their zero divisors. In this study, we consider a class of 3-radical zero completely primary finite rings whose diameter and girth are 2 and 3 respectively. We enhance the understanding of the structure of such rings by investigating their Adjacency, Laplacian and Distance matrices.

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