A Note on the Commutativity of Prime Near-rings  

作　　者：Yilun Shang 

机构地区：[1]Institute for Cyber Security, University of Texas at San Antonio San Antonio, Texas 78249, USA

出　　处：《Algebra Colloquium》2015年第3期361-366,共6页代数集刊（英文版）

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.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.

关 键 词：NEAR-RING DERIVATION prime graph 

分 类 号：O153.3[理学—数学] P283.1[理学—基础数学]