一类分配生成素近环成为交换整区的条件

The conditions for some distributively generated prime near-ring being a commutative domain

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 .证明了 :如果N满足下列条件之一 ,则N是交换整区 .(1)N容纳两个非零导子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 .

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 ore of the following conditions: (1)N admits two non-zero derivations D 1,D 2 such that D 1D 2(N)Z, (2) N admits a non-zero derivation D such that [D(N),D 2(N)]=0 .