Commutativity of some Prime Nearrings using Left-Sided outer (σ, τ)-n-Derivation
DOI:
https://doi.org/10.56919/usci.2324.013Keywords:
Commutativity, Derivations, Nearrings, Outer (σ, τ)-n-derivation, Prime nearringsAbstract
In the field of mathematics, pure mathematics is very important as it gives rise to the basis for the formation of all applicable mathematical concepts in solving real-life problems. Algebra is such an integral part of pure mathematics. It consists of the Ring theory. It has been discovered that there exists some structures similar to rings with little deformity and they are called NEARRINGS. These structures do not commute mostly as they fail to satisfy distributive law. To ascertain the commutativity of nearrings, we need derivation(s). Because several papers had been presented dealing with left-nearrings, this paper aimed to consider right-nearrings which has not been done before in that respect, to the best of our knowledge. Some methods dealing with left-nearrings have been studied and modified in this work, and new derivation has been introduced to take care of right-nearrings. For Let 
be a positive integer, 
be a right nearring, and automorphisms
, in this study, the concept of left-sided outer (σ, τ)--derivations on the nearrings is introduced, and several features are examined to show commutativity of prime right nearring using the derivation. The results obtained in this paper show that the right-nearrings are commutative when subjected to derivation.
References
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