Automorphisms of Zero Divisor Graphs of Cube Radical Zero Completely Primary Finite Rings
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Published
Dec 24, 2020
Page:
83-90
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Lao Hussein Mude
Department of Mathematics and Computer Science, University of Kabianga, P. O. Box 2030-20200, Kericho, Kenya
Owino Maurice Oduor
Department of Mathematics and Computer Science, University of Kabianga, P. O. Box 2030-20200, Kericho, Kenya.
Ojiema Michael Onyango
Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya
Abstract
One of the most interesting areas of research that has attracted the attention of many scholars are theory of zero divisor graphs. Most recent research have focused on properties of zero divisor graphs with little attention given on the automorphsisms, despite the fact that automorphisms are useful in interpreting the symmetries of algebraic structure. Let R be a commutative unital finite rings and Z(R) be its set of zero divisors. In this study, the automorphisms zero divisor graphs of such rings in which the product of any three zero divisor is zero has been determined.
Keywords:
Automorphisms, zero divisor graphs, completely primary finite rings.
Article Details
How to Cite
Mude, L. H., Oduor, O. M., & Onyango, O. M. (2020). Automorphisms of Zero Divisor Graphs of Cube Radical Zero Completely Primary Finite Rings. Journal of Advances in Mathematics and Computer Science, 35(8), 83-90. https://doi.org/10.9734/jamcs/2020/v35i830316
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Original Research Article
References
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Chikunji J. Automorphism groups of finite rings of characteristic p2 and p3. Glasnik Matematicki. 2008;43(63):25-40.
Lao H. Mude, Owino M. Oduor, Ojiema M. Onyango. Automorphisms of zero divisor graphs of square radical zero commutative unital finite rings. 2020;19:2347-1921.
Owino M. Oduor, Ojiema M. Onyango, Mmasi Eliud. Units of commutative completely primary finite rings of characteristic pn. International Journal of Algebra. 2016;7(6).
Lao H. Mude, Owino M. Oduor, Ojiema M. Onyango. Automorphisms of zero divisor graphs of Galois rings. 2020;8:401- 406. [5] Chikunji J. Automorphisms of completely primary finite rings of characteristic p. Colloq. Mathematica. 2008;111:91-103.
Chikunji J. Unit groups of cube radical zero commutative completely primary finite rings. International Journal of Mathematics and Mathematical Sciences. 2005;4:579-592.
Chikunji J. Unit groups of a certain class of completely primary finite completely primary finite rings. Mathematical Journal of Okayama University. 2005;47:39-53.
Chikunji J. On unit groups of completely primary finite completely primary finite rings. Mathematical Journal of Okayama University. 2008;50:149-160.
Chikunji J. A classification of cube radical completely primary finite rings. Demonstratio Mathematica. 2005;XXXVIII(1):7-20.
Chikunji J. Automorphism groups of finite rings of characteristic p2 and p3. Glasnik Matematicki. 2008;43(63):25-40.