素近环上的理想和中心化映射  

Ideal and centralizing mappings in prime near-rings

作　　者：金晓灿[1] 

机构地区：[1]南京理工大学理学院,江苏南京210094

出　　处：《信阳师范学院学报（自然科学版）》2004年第2期131-133,共3页Journal of Xinyang Normal University(Natural Science Edition)

摘　　要：设N是零对称的素近环,Z是其乘法中心,U是N的一个非零理想.证明了:若T是N上的一个非平凡自同构或导子,使得 u∈U,[u,T(u)]∈Z,且T(u)∈U,则当理想U是分配时,N是交换素环,且若N是2-挠自由的分配素近环,则N只须为一约当理想即可.Let N be zero-symmetric prime near-ring and Z the center of N,U be a nonzero ideal of N.It is shown that if T is a nontrivial automorphism of N such that [u,T(u)]∈Z,and T(u) is in U for every u in U,and if U is distributive,then N is a commutive prime ring.And if N is a 2-torision free distributive prime near-ring,then U need only be a nonzero Jordan ideal.

关 键 词：素近环 理想 中心化映射 自同构 导子 挠自由 交换子 

分 类 号：O153.3[理学—数学]