带有对合的素环的微分恒等式  

Differential Identities in Prime Rings with Involution

作　　者：黄述亮 HUANG Shu-liang(School of Mathematics and Finance,Chuzhou University,Chuzhou 239000,China)

机构地区：[1]School of Mathematics and Finance,Chuzhou University,Chuzhou 239000,China

出　　处：《Chinese Quarterly Journal of Mathematics》2023年第2期134-144,共11页数学季刊（英文版）

基　　金：Supported by the University Science Research Project of Anhui Province(Grant Nos.KJ2020A0711,KJ2020ZD74,KJ2021A1096);the Natural Science Foundation of Anhui Province(Grant No.1908085MA03)。

摘　　要：Let R be a prime ring of characteristic different from two with the second involution∗andαan automorphism of R.An additive mapping F of R is called a generalized(α,α)-derivation on R if there exists an(α,α)-derivation d of R such that F(xy)=F(x)α(y)+α(x)d(y)holds for all x,y∈R.The paper deals with the study of some commutativity criteria for prime rings with involution.Precisely,we describe the structure of R admitting a generalized(α,α)-derivation F satisfying any one of the following properties:(i)F(xx∗)−α(xx∗)∈Z(R),(ii)F(xx∗)+α(xx∗)∈Z(R),(iii)F(x)F(x∗)−α(xx∗)∈Z(R),(iv)F(x)F(x∗)+α(xx∗)∈Z(R),(v)F(xx∗)−F(x)F(x∗)∈Z(R),(vi)F(xx∗)−F(x∗)F(x)=0 for all x∈R.Also,some examples are given to demonstrate that the restriction of the various results is not superfluous.In fact,our results unify and extend several well known theorems in literature.

关 键 词：Prime rings Generalized(α α)-derivations INVOLUTION COMMUTATIVITY 

分 类 号：O153.3[理学—数学]