Commutativity of Near-rings with Derivations-Reference-Cited by-同舟云学术

Commutativity of Near-rings with Derivations

Published:2014-04-11 Issue:02 Volume:21 Page:215-230
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Kamal Ahmed A. M.¹,Al-Shaalan Khalid H.¹

Affiliation:

1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Kingdom of Saudi Arabia

Abstract

In this paper we first prove that a near-ring admits a derivation if and only if it is zero-symmetric. Also, we prove some commutativity theorems for a non-necessarily 3-prime near-ring R with a suitably-constrained derivation d satisfying the condition that d(a) is not a left zero-divisor in R for some a ∈ R. As consequences, we generalize several commutativity theorems for 3-prime near-rings admitting derivations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386714000170

Reference23 articles.

1. Commutativity of rings satisfying some polynomial conditions

2. On weakly periodic-like rings and commutativity theorems

3. Posner and herstein theorems for derivations of 3-prime near-rings

4. On some commutativity theorems of Herstein

5. A Commutativity Theorem for Near-Rings

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Commutativity Conditions for Rings and Generalized 2-CN Rings;Algebra Colloquium;2021-01-20

2. On some properties of near-rings;Arabian Journal of Mathematics;2020-11-22

3. Some properties of rings and near-rings with derivations and generalized derivations;Georgian Mathematical Journal;2020-01-17

4. The commutative ring for prime near-rings by involving derivation;Journal of Physics: Conference Series;2019-05-01

5. On commutativity of near-rings with generalized derivations;Indian Journal of Pure and Applied Mathematics;2017-06