可成为交换整区的素近环  

Prime Near-rings That can Being a Commutative Domain

作　　者：金晓灿[1] 

机构地区：[1]南京理工大学理学院,南京210094

出　　处：《南京理工大学学报》2003年第z1期69-72,共4页Journal of Nanjing University of Science and Technology

摘　　要：设N是2-挠自由分配生成素近环,它具有单位元1和中心Z。该文证明了如果N,满足下列条件之一,则N是交换整区:(1)N容纳2个非零导子D1,D2,使得D1D2(N)Z;(2)N容纳一个非零导子D,使得[D(N),D2(N)]={0};(3)N容纳一个导子D,使得D(Z)≠{0},且x,y∈N,有[x-D(x),D(y)]=0。Let N be a 2 - torision free distributively generated near-ring with identity 1 and the center Z . It is shown that N is a commutative domain if it satisfies one of the following con-ditions:(1) N admits two non-zero derivations D1 ,D2 ,such that D1 ,D2(N) Z; (2) N admits a non-zero derivations D such that [D(N),D2(N)] = {0} ;(3) N admits a derivation D such that D(Z)≠ {0} and [x - D(x),D(y)] = 0,x,y ∈ N.

关 键 词：导子 分配生成 素近环 挠自由 换位子 

分 类 号：O152[理学—数学]