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 N be a prime near-ring. We show two main results on the commutativity of N： （1） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（[x,y]） = xk[x,y]xl for all x,y ∈ N o...Let N be a prime near-ring. We show two main results on the commutativity of N： （1） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（[x,y]） = xk[x,y]xl for all x,y ∈ N or D（[x,y]） = -xk[x,y]xI for all x,y ∈ N, then N is a commutative ring. （2） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（x o y） = xk（x o y）xl for all x, y ∈ N or D（x o y） = -xk（x o y）xl for all x, y ∈ N, then N is a commutative ring. Moreover, some interesting relations between the prime graph and zero-divisor graph of N are studied.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.
文摘Let N be a prime near-ring. We show two main results on the commutativity of N： （1） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（[x,y]） = xk[x,y]xl for all x,y ∈ N or D（[x,y]） = -xk[x,y]xI for all x,y ∈ N, then N is a commutative ring. （2） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（x o y） = xk（x o y）xl for all x, y ∈ N or D（x o y） = -xk（x o y）xl for all x, y ∈ N, then N is a commutative ring. Moreover, some interesting relations between the prime graph and zero-divisor graph of N are studied.
