Automorphisms of Zero Divisor Graphs of Cube Radical Zero Completely Primary Finite Rings

Lao Hussein Mude; Owino Maurice Oduor; Ojiema Michael Onyango

doi:10.9734/jamcs/2020/v35i830316

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Automorphisms of Zero Divisor Graphs of Cube Radical Zero Completely Primary Finite Rings

Lao Hussein Mude

Owino Maurice Oduor

Ojiema Michael Onyango

Journal of Advances in Mathematics and Computer Science, Page 83-90
DOI: 10.9734/jamcs/2020/v35i830316
Published: 24 December 2020

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.

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

References

Ojiema O, Owino M, Odhiambo P. Automorphisms of unit groups of square radical zero finite commutative completely primary finite ring. Pure mathematic Sciences. 2016;5(1):11-23.

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.

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