素环和半素环上的对称斜反n-阶导子  

Prime And Semiprime Rings with Symmetric Skew Reverse n-derivation

作　　者：霍东华 刘红玉 HUO Dong-hua;LIU Hong-yu(School of Mathematical Sciences,Mudanjiang Normal University,Mudanjiang 157012,China)

机构地区：[1]牡丹江师范学院数学科学学院,黑龙江牡丹江157012

出　　处：《数学的实践与认识》2020年第21期187-193,共7页Mathematics in Practice and Theory

基　　金：黑龙江省教育厅基本科研业务费项目(1354ZD007);牡丹江师范学院国家级课题培育项目(GP2020005)。

摘　　要：设n≥2是一个固定的正整数,R是非交换的n!-无挠半素环,L是R的非零双边理想,α和β是R的两个反自同构,△:Rn→R是与反自同构α和β相关的对称的斜反n-阶导子.假设△的迹函数δ在L上是β-可交换的并且对任意的x∈L有[δ(x),α(x)]∈Z(R).则对任意的x∈L有[δ(x),α(x)]=0.如果R是n!-无挠的素环并且△≠0也有同样的假设,则R是交换环.Let n≥2 be a fixed positive integer and let R be a noncommutative n!-torsion free semiprime ring,L be a nonzero two-sided ideal of R,α and β are two antiautomorphism of R and △:R^n→R be a symmetric skew reverse n-derivation associated with the antiautomorphism α and β.Suppose that the trace function δ of △ is β-commuting on L and [δ(x),α(x)] E Z(R) for all x ∈ L.Then [δ(x),α(x)]=0 for all x ∈ L.If R is a n!-torsion free prime ring and △ ≠0 under the same condition,then R is commutative ring.

关 键 词：素环 半素环 对称斜反n-阶导子 中心映射 交换映射 

分 类 号：O153.3[理学—数学]