摘要
本文给出了带求导的3-素近环的若干性质．
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 M of (N, +)is invariant if NM M and MN M.In thispaper.the author proves the following theorems:Theorem 1. Let N be a zero-symmetric 3-prime near-ring with a nonzero derivation dand M a nonzero invariant subnear-ring of N such that d (M) Z(N) .where Z(N) = {x∈N|nx=xn for all n∈N}' Then N is a commutative ring without nontrivial zero divisors.Theorem 2. Let N be a zero-symmetrit 3-prime near-ring with a nonzero derivation dand a∈N. Suppose that M is a nonzero invariant subnear-ring of N such that 2M≠0 and d(x)a=ad(x) for all x∈M. Then a∈Z(N).Theorem 3. Let N be a zero-symmetric 3-prime near-ring with nonzero derivations d1,,d2,and δ. Suppose that M is a nonzero invariant subnear-ring of N such that 2M≠0,d1δ(M)≠0 and δ(y)d1 (x) =d,(x)δ(y) for all x,y∈M. Then N is a commutative ring without nontrivial zero divisors.
出处
《湖南教育学院学报》
1997年第2期1-5,共5页
Journal of Hunan Educational Institute
