素近环上的理想和中心化映射

Ideal and centralizing mappings in prime near-rings

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.