素近环上的理想和中心化映射  

Ideal and centralizing mapping 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：《黄冈师范学院学报》2003年第6期24-25,28,共3页Journal of Huanggang Normal University

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.我们将证明: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 a zero-symmetric prime near-ring and Z be its center, U be a nonzero ideal of N. We will show that: If T is a nontrivial automorphism of N such that ∈Z and T(u) is in U for every u in U. Then if U is distributive, N is a commutive prime ring. And if N is a 2-torision free distributive prime near-ring, then N can be only 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]