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 Bre...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.展开更多
In this paper,supersemiprime ring is introduced,relations among the supersemiprime rings and the some rings around it are discussed,supersemiprime radical and its properties are studied.
The aim of this paper is to define the notions of generalized （m, n）-derivations and generalized （m, n）：Jordan derivations and to prove two theorems involving these map- pings.
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 identi...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.展开更多
Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF...Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.展开更多
In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Fi...In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.展开更多
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.
Let R be a prime ring with center Z, 5 ： R → R a nonzero skew derivation, and n a fixed positive integer. In this paper, we show that R is a commutative ring if （i） [（δ（[x, y]）, [x, y]]n = 0 for all x, y ∈ R ...Let R be a prime ring with center Z, 5 ： R → R a nonzero skew derivation, and n a fixed positive integer. In this paper, we show that R is a commutative ring if （i） [（δ（[x, y]）, [x, y]]n = 0 for all x, y ∈ R or （ii） [（δ（x）, x]n e Z for all x ∈ R, except some specific cases.展开更多
Let G be an arbitrary group with identity e. Let A be a G-graded ring with identity 1, i. e. A= A<sub>g</sub> （direct sums of additive groups）, with property A<sub>g</sub>A<sub>h</su...Let G be an arbitrary group with identity e. Let A be a G-graded ring with identity 1, i. e. A= A<sub>g</sub> （direct sums of additive groups）, with property A<sub>g</sub>A<sub>h</sub> A<sub>gh</sub>. The smash prod-展开更多
文摘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.
文摘In this paper,supersemiprime ring is introduced,relations among the supersemiprime rings and the some rings around it are discussed,supersemiprime radical and its properties are studied.
文摘The aim of this paper is to define the notions of generalized （m, n）-derivations and generalized （m, n）：Jordan derivations and to prove two theorems involving these map- pings.
基金Partially supported by China Postdoctoral Science Foundation
文摘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.
文摘Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.
文摘In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.
文摘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.
文摘Let R be a prime ring with center Z, 5 ： R → R a nonzero skew derivation, and n a fixed positive integer. In this paper, we show that R is a commutative ring if （i） [（δ（[x, y]）, [x, y]]n = 0 for all x, y ∈ R or （ii） [（δ（x）, x]n e Z for all x ∈ R, except some specific cases.
文摘Let G be an arbitrary group with identity e. Let A be a G-graded ring with identity 1, i. e. A= A<sub>g</sub> （direct sums of additive groups）, with property A<sub>g</sub>A<sub>h</sub> A<sub>gh</sub>. The smash prod-
