Open AccessON COMMUTATIVITY OF PRIME NEAR RINGS
Author(s) -
Abdul Rauf Khan,
Khadija Mumtaz,
Muhammad Waqas
Publication year - 2021
Publication title -
matrix science mathematic
Language(s) - English
Resource type - Journals
eISSN - 2521-084X
pISSN - 2521-0831
DOI - 10.26480/msmk.01.2021.06.15
Subject(s) - prime (order theory) , homomorphism , commutative property , mathematics , commutative ring , prime ring , zero (linguistics) , combinatorics , physics , discrete mathematics , linguistics , philosophy
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