素环上导子的线性组合

In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen.Our aim is to improve Niu‘s result.For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest.  

素GPI-环广义形心扩张的本原性

类似于中心扩张，本文引入了广义形心扩张的概念，且研究了广义形心扩张的本原性。  

Smash Product， Morita Context Rings and Extended Centroids

ＳｍａｓｈＰｒｏｄｕｃｔ，ＭｏｒｉｔａＣｏｎｔｅｘｔＲｉｎｇｓａｎｄＥｘｔｅｎｄｅｄＣｅｎｔｒｏｉｄｓ￥ＹａｎｇＳｈｉｌｉｎ杨士林（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＣｏｍｐｕｔｅｒＩｎｓｔｉｔｕｔｅ，Ｂｅｉｊｉｎｇ，１０...  

素GPI-环的幂零多项式

R是素GPI-环,若多项式f(x1,…,xd)在R上是幂零的,则或f(x1,…,xd)是R的恒等式,或R是有限域上的有限矩阵环.  

素GPI-环的幂零多项式

Ｒ是素ＧＰＩ－环，若多项式ｆ（ｘ_１，…，ｘ_d）在Ｒ上是幂零的，则或ｆ（ｘ_１…，ｘ_d）是Ｒ的恒 等式，或Ｒ是有限域上的有限矩阵环  

Derivations with power central values on multilinear polynomials in prime rings

Let R be a prime ring of char R ≠ = 2 with center Z(R) and with extended centroid C, d a nonzero derivation of R and f(x ₁, ..., x _n ) a nonzero multilinear polynomial over C. Suppose that x ^s d(x)x ^t ∈ Z(R) for all x ∈ {d(f(x ₁, ..., x _n ))|x ₁, ..., x _n ∈ ρ}, where ρ is a nonzero right ideal of R and s ≥ 0, t ≥ 0 are fixed integers. If d(ρ)ρ ≠ = 0, then ρ C = eRC for some idempotent e in the socle of RC and f(x ₁, ..., x _n ) ^N is central-valued in eRCe, where N = s + t + 1.   

Vanishing power values of commutators with derivations

Let R be a prime ring of char R ≠ 2, let d be a nonzero derivation of R, and let ρ be a nonzero right ideal of R such that [[d(x)x ⁿ , d(y)] _m , [y, x] _s ] ^t = 0 for all x, y є ρ, where n ≥ 1, m ≥ 0, s ≥ 0, and t ≥ 1 are fixed integers. If [ρ, ρ]ρ ≠ 0 then d(ρ)ρ = 0.