Commutativity of Near-rings with Derivations  

作　　者：Ahmed A.M. Kamal Khalid H. AI-Shaalan 

机构地区：[1]Department of Mathematics, College of Science, King Saud University P.O. Box 2455, Riyadh 11451, Kingdom of Saudi Arabia

出　　处：《Algebra Colloquium》2014年第2期215-230,共16页代数集刊（英文版）

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.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.

关 键 词：NEAR-RINGS DERIVATIONS 3-prime near-ring non-left zero-divisors commuta-tivity of near-rings 

分 类 号：O153.3[理学—数学]