Commutativity of Near-rings with Derivations

• 作者: Ahmed A.M. Kamal Khalid H. AI-Shaalan
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 交换性定理 素近环 导子 左零因子 证明
• 年，卷（期）: 2014,（2）
• 页码范围: 215-230
• 页数: 16页
• 分类号: O153.3
• 语种: 中文

摘要

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.