Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the stru...Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.展开更多
Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф（Xi^△j） is a reduced generalized differential identity for an essential ideal of R, then ф（Zije（△j ）） is a ...Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф（Xi^△j） is a reduced generalized differential identity for an essential ideal of R, then ф（Zije（△j ）） is a generalized polynomial identity for RF, where e（△j） are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф（Xi△j） is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф（Zij） is a generalized polynomial identity for [R, R]. Moreover, if ф（Xi△j） is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф（Zij） is a generalized polynomial identity for Q.展开更多
为了促进交换性的发展,根据半质环及半单环的相关资料,扩展了文献[1-2]的结论,得出了环的两个交换性定理:定理1:设R为一个半质环,若对▽x1,x2,…,xn∈R,有依赖于x1,x2的整系数多项式p(t)使得[…[[x1-x12p(x1),x2],x3],…,xn]∈Z(R),则R...为了促进交换性的发展,根据半质环及半单环的相关资料,扩展了文献[1-2]的结论,得出了环的两个交换性定理:定理1:设R为一个半质环,若对▽x1,x2,…,xn∈R,有依赖于x1,x2的整系数多项式p(t)使得[…[[x1-x12p(x1),x2],x3],…,xn]∈Z(R),则R为交换环。定理2:设R为一个kothe半单纯环,若对▽a,b,x2,…,xn∈R都有一正整数K=K(a,b),一含有x2和n=n(a,b)(≥K)个y的字fx(x,y)及一整系数多项式φx(x,y)使得[…[[∑ki=0αi bi abk-i-fx(a,b)φx(a,b),x2],x3],…,xn]∈Z(R)其中|∑ki=0αi|=1,则R为交换环.展开更多
基金China NNSF (10726051)Grant in-aid for Scientific Research from Department of Mathematics,Jilin University
文摘Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.
基金supported by the mathematical Tianyuan Research Foundation of China(10426005)the Basic Research Foundation of Beijing Institute of Technology of China
文摘Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф（Xi^△j） is a reduced generalized differential identity for an essential ideal of R, then ф（Zije（△j ）） is a generalized polynomial identity for RF, where e（△j） are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф（Xi△j） is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф（Zij） is a generalized polynomial identity for [R, R]. Moreover, if ф（Xi△j） is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф（Zij） is a generalized polynomial identity for Q.
文摘为了促进交换性的发展,根据半质环及半单环的相关资料,扩展了文献[1-2]的结论,得出了环的两个交换性定理:定理1:设R为一个半质环,若对▽x1,x2,…,xn∈R,有依赖于x1,x2的整系数多项式p(t)使得[…[[x1-x12p(x1),x2],x3],…,xn]∈Z(R),则R为交换环。定理2:设R为一个kothe半单纯环,若对▽a,b,x2,…,xn∈R都有一正整数K=K(a,b),一含有x2和n=n(a,b)(≥K)个y的字fx(x,y)及一整系数多项式φx(x,y)使得[…[[∑ki=0αi bi abk-i-fx(a,b)φx(a,b),x2],x3],…,xn]∈Z(R)其中|∑ki=0αi|=1,则R为交换环.
