摘要
本文证明了如下如果:设N是零对称3—素近环,U是N的一个非零不变子近环,d是N的一个非平凡求导,如果且,那么以下条件等价:(1)对每个是N的乘法中心元,(2)对所有有是一个无零因子交换环。
A near-ring N is called 3-prime if aNb=0 implies a=0 or b=0 for a, b∈N. An endomorphism d of (N, +) is called a derivation on N if it satisfies d(xy)=xd(y)+d(x)y for all x,y∈N. A subgroup U of (N, +)is invariant if NUU and UNU. Let N be a zero-symmetric -prime near-ring with nonzero derivation d and U a nonzero invariant subnear-ring of N such that d(U)UN_d and 2U≠0. It is shown that the following are equivalent: (1)For each u∈U, d^2(u) is in the multiplicative centre of N; (2)For all u∈U, [d(u), d(v)]=0; (3)N is a commutative ring without nontrivial zero divisors.
出处
《湖南教育学院学报》
1995年第5期8-12,共5页
Journal of Hunan Educational Institute
