On Automorphisms and Commutativity in Semiprime Rings

Canadian mathematical bulletin

Pao-Kuei Liau¹  Cheng-Kai Liu¹ 

[1] Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan

关键词: automorphism;    generalized polynomial identity (GPI);   

DOI  :  10.4153/CMB-2011-185-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $R$ be a semiprime ring with center$Z(R)$. For $x,yin R$, we denote by $[x,y]=xy-yx$ the commutator of$x$ and $y$. If $sigma$ is a non-identity automorphism of $R$ suchthat $$Big[ig[dotsig[[sigma(x^{n_0}),x^{n_1}],x^{n_2}ig],dotsig],x^{n_k}Big]=0$$for all $x in R$, where $n_{0},n_{1},n_{2},dots,n_{k}$ are fixedpositive integers, then there exists a map $mucolon Rightarrow Z(R)$such that $sigma(x)=x+mu(x)$ for all $xin R$. In particular, when$R$ is a prime ring, $R$ is commutative.

【 授权许可】

Unknown