ABSTRACT
ON COMMUTATIVITY OF PRIME NEAR RINGS
Journal: Matrix Science Mathematic (MSMK)
Author: Abdul Rauf Khan, Khadija Mumtaz, 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.01.2021.06.15
In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a zero symmetric prime near ring. If there exist p ≥ 0, q ≥ 0 and a nonzero two sided β-derivation d on M, where β : M → M is a homomorphism, such that d satisfy one of the following conditions:
- [β(s),d(t)] = sp(β(s)oβ(t))sq ∀ s, t ∈ M
- [β(s),d(t)] = −sp(β(s)oβ(t))sq ∀ s, t ∈ M
- [d(s),β(t)] = tp(β(s)oβ(t))tq ∀ s, t ∈ M
- [d(s),β(t)] = −tp(β(s)oβ(t)tq ∀ s, t ∈ M
| Pages | 06-15 |
| Year | 2021 |
| Issue | 1 |
| Volume | 5 |
