素环上的导子在Lie理想上的协交换子的零化子

Let R be a prime ring of characteristic different from 2,d and g twoderivations of R at least one of which is nonzero,L a non-central Lie ideal of R,anda∈R.We prove that if a(d(u)u-ug(u))=0 for any u∈L,then either a=0,or R is an s_4-ring,d(x)=[p,x],and g(x)=-d(x)for some p in the Martindalequotient ring of R.     

On Lie Ideals and Automorphisms in Prime Rings

Mathematical Notes - Let R be a prime ring of characteristic different from 2 with center Z and extended centroid C, and let L be a Lie ideal of R. Consider two nontrivial automorphisms α and...     

On Jordan Left Derivations of Lie Ideals in Prime Rings

Let R be a prime ring with characteristic different from two and U be a Lie ideal of R such that u² U for all u U. In the present paper it is shown that if d is an additive mappings of R into itself satisfying d(u²) = 2ud(u), for all u U, then either U Z(R) or d(U) = (0).1991 Mathematics Subject Classification 16W25 16N60     

特征为2的素环的Lie理想上中心化自同构

Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that [x^σ,x] E Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R)=2 and dimc RC = 4.     

On Lie Automorphisms,Additive Subgroups,and Lie Ideals of Prime Rings

Abstract

Let R be a prime ring of characteristic not equal to 2 or 3 and let L be a noncentral Lie ideal of R. Suppose that σ is a Lie automorphism on L such that σ⁴ is not the identity map. Then the additive subgroup generated by the set {[x ^σ, x] ∣ x ∈ L} contains a noncentral Lie ideal of R.     

环中的粗素理想与模糊粗素理想

首次提出了环中的粗素理想与模糊粗素理想的概念，并讨论了它的性质及同态问题。     

A Note on Commutators with Power Central Values on Lie Ideals

This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d（u）,u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis＇s results.     

Power Values of Generalized Derivations with Annihilator Conditions in Prime Rings

Let R be a prime ring, H a nonzero generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that there exists ${0 \neq a \in R}$ such that a(u ^s H(u)u ^t ) ⁿ = 0 for all ${u \in L}$ , where s ≥ 0, t ≥ 0, n ≥ 1 are fixed integers. Then s = 0, H(x) = bx for all ${x \in R}$ with ab = 0, unless R satisfies s ₄, the standard identity in four variables. We also describe completely this last case.