共查询到15条相似文献,搜索用时 62 毫秒
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设R是半素环,U是R的极大右商环,C是R的扩展型心,a,b∈U.对R上广义导子δ的值的幂零,幂中心化子问题进行了讨论,即(aδ(x))~nb=0(∈C)形式的恒等式,对δ的形式以及δ与a,b的关系做了完整的刻画,从而发展了Herstein,Brear的研究结果. 相似文献
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Let R be a prime ring with a non-central Lie ideal L. In the present paper we show that if the composition DG of two generalized derivations D and G is zero on L, then DG must be zero on R. And we get all the possibilities for the composition of a couple of generalized derivations to be zero on a non-central Lie ideal of a prime ring. 相似文献
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齐霄霏 《数学物理学报(A辑)》2014,34(2):463-472
设L是Banach空间X上的J-子空间格,AlgL是相应的(J-子空间格代数.设φ:AlgL→AlgL是可加映射,对每个K∈(J)(L),dimK≥2.该文证明了下列表述等价:(1)φ是中心化子;(2)φ满足AB=0■φ(A)B=Aφ(B)=0;(3)φ满足AB+BA=0■φ(A)B+φ(B)A=Aφ(B)+Bφ(A)=0;(4)φ满足ABC+CBA=0■φ(A)BC+φ(C)BA=ABφ(C)+CBφ(A)=0.作为应用,得到AlgL上在零点广义可导的可加映射的完全刻画. 相似文献
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Let R be a prime ring with center Z(R), I a nonzero ideal of R, d a nonzero derivation of R and 0≠a∈ R. In the present paper, our object is to study the situation a[d(xk), xk]n∈ Z(R) for all x ∈ I under certain conditions, where n(≥ 1), k(≥ 1) are fixed integers. 相似文献
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设g=g(A,M,N,B)是平凡的广义矩阵代数,Ω是g中任意但固定的一点.本文证明了在一定条件下,线性映射φ对满足ST=Ω的S,T∈g有φ(Ω)=φ(S)T=Sφ(T)当且仅当φ是g上的中心化子. 相似文献
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利用导子和triple导子的定义,刻画了特征不等于2的代数闭域上4维幂零李代数的导子和triple导子. 相似文献
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This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al. 相似文献
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Let R be a prime ring with center Z and S (?) R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x-xG(x) ∈ Z for all x ∈ S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime case is also considered. 相似文献
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The concept of derivations and generalized inner derivations has been generalized as an additive function δ: R→ R satisfying δ(xy) = δ(x)y xd(y) for all x,y∈R,where d is a derivation on R.Such a function δis called a generalized derivation.Suppose that U is a Lie ideal of R such that u2 ∈ U for all u ∈U.In this paper,we prove that U(C)Z(R) when one of the following holds:(1)δ([u,v]) = uov (2)δ([u,v]) uov=O(3)δ(uov) =[u,v](4)δ(uov) [u,v]= O for all u,v ∈U. 相似文献
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Jui-Chi Chang 《代数通讯》2013,41(6):2241-2248
Let R be a prime ring with center Z and L a noncommutative Lie ideal of R. Suppose that f is a right generalized β-derivation of R associated with a β-derivation δ such that f(x) n ∈ Z for all x ∈ L, where n is a fixed positive integer. Then f = 0 unless dim C RC = 4. 相似文献