关于素数近环的广义β-导数交换性的一个注记

Matrix Science Mathematic Pub Date : 2021-03-15 DOI:10.26480/msmk.01.2021.16.19

Abdul Rauf Khan, Khadija Mumtaz, Muhammad Mohsin Waqas

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引用次数: 0

摘要

本文利用β-导子的概念证明了素数近环的交换性。设M是素数近环。如果M上存在与非零双侧β-导数相关的双侧广义β-导数G，其中是同态，满足以下条件：G（[p_1，q_1]）=〖p_1〗^（u1）[β（p1），β（q_1）]〖p_1〕^（v_1）那么M是一个可交换环。

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A NOTE ON COMMUTATIVITY OF PRIME NEAR RING WITH GENERALIZED β-DERIVATION

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.

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Matrix Science Mathematic

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审稿时长

12 weeks