摘要
设N是一个2—挠自由分配生成素近环,它具有单位元1和中心Z。本文证明了;如果N满足下列条件之一,则N是交换整区:(1)N容纳一个非零导子D使得容纳一个非零导子D使得x,y∈N,[D(x),D2(y)]=0,并且D(N)不含非零的幂零元.
Let N be a 2-torsion-free distributively generated prime near-ring with identity 1 and the center Z. It is shown that N is a commutative domain if it satisfies one of the following conditions: (l ) N admits a nonzero derivation D such that D2(N) Z ; (2)N admits anonzero derivation D such that[ D(x), D2 (y) ]= 0,x,y ∈ N, and D(N) haven't nonzero nilpotent elements.
出处
《湖北大学学报(自然科学版)》
CAS
1994年第2期135-138,共4页
Journal of Hubei University:Natural Science
关键词
导子
分配生成
素近环
交换子
环论
Derivation Distributively generated prime near-ring Torsion-free Commutator Localization