摘要
设 N是中心为 Z的素近环 ,I是 N的右理想 ,D是 N上的非平凡导子 .本文证明了 :( i)若 D( I) Z,则 ( N1 +)是交换的 ;又若 N 2 -挠自由 ,则 N是无零因子交换环 .( ii)若 0≠ Dn( I) Z,Dn- 1 ( I) I,且 N是 ( n +1 ) !-挠自由的 ,则
Let N be a prime near- ring with center Z, I a right ideal of N,D a non- trival derivations of N. We proved:(i) If D(I)Z,I≠{0}, then (N ,+) is abelian. Moreover, if N is 2- torsion- free, then N is an integ ral ring. (ii) If Dn(I)Z,D n-1 (I)I,N is (n+1)! - torsion- free ,then either D(I)={0} or N is an integral ring.
出处
《应用数学》
CSCD
2000年第1期98-101,共4页
Mathematica Applicata
