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.
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
关键词
素近环
理想
中心化映射
自同构
导子
挠自由
交换子
prime near-ring
ideal
centralizing mapping
automorphism
derivation
torision free
commutator
