ABSTRACT
A NOTE ON β-DERIVATIONS IN PRIME NEAR RING
Journal: Matrix Science Mathematic (MSMK)
Author: Abdul Rauf Khan, Khadija Mumtaz and Muhammad Mohsin Waqas
This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
DOI: 10.26480/msmk.01.2021.20.23
In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a prime near ring. If there exist p,q ϵ M and two sided nonzero β-derivation f on M, where β:M→M is a homomorphism, satisfying the following conditions:
f([s,t])=s^p [β(s),β(t)]s^q ∀ s,t ϵ M
f([s,t])=-s^p [β(s),β(t)]s^q ∀ s,t ϵ M
| Pages | 20-23 |
| Year | 2021 |
| Issue | 1 |
| Volume | 5 |
