A Note on the Commutativity of Prime Near-rings

• 作者: Yilun Shang
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 交换性 素近环 注记 交换环 因子图 广义 素图
• 年，卷（期）: 2015,（3）
• 页码范围: 361-366
• 页数: 6页
• 分类号: O153.3
• 语种: 中文

摘要

Let N be a prime near-ring. We show two main results on the commutativity of N: (1) If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D([x,y]) = xk[x,y]xl for all x,y ∈ N or D([x,y]) = -xk[x,y]xI for all x,y ∈ N, then N is a commutative ring. (2) If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D(x o y) = xk(x o y)xl for all x, y ∈ N or D(x o y) = -xk(x o y)xl for all x, y ∈ N, then N is a commutative ring. Moreover, some interesting relations between the prime graph and zero-divisor graph of N are studied.