ABSTRACT
A NOTE ON COMMUTATIVITY OF PRIME NEAR RING WITH GENERALIZED β-DERIVATION
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.01.2021.16.19
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 and two sided generalized β-derivation G associated with the non-zero two sided β-derivation on M, where is a homomorphism, satisfying the following conditions:
- G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 ϵ M
- G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 ϵ M
Then M is a commutative ring.
| Pages | 16-19 |
| Year | 2021 |
| Issue | 1 |
| Volume | 5 |
