2-扭自由素环上的左(θ,θ)-导子  

Left(θ,θ)-Derivations of 2-torsion Free Prime Ring

作　　者：路春雪 LU Chunxue(Graduate School of Jilin Normal University,Changchun,Jilin Province,130000 China)

机构地区：[1]吉林师范大学研究生院,吉林长春130000

出　　处：《科技资讯》2022年第8期202-204,共3页Science & Technology Information

摘　　要：环论是代数学的重要组成部分,导子理论是算子代数的重要研究内容。通过环上的导子的性质探索不同环的结构一直是热门研究课题。随着环理论的不断发展,环上的导子也被不断丰富和扩展,并且相继出现了许多衍生导子,如广义导子、左导子、广义(θ,θ)-导子及左(θ,θ)-导子等。该文以左(θ,θ)-导子的定义为切入点,采用代数学中的常用方法替换法讨论了2-扭自由素环的Lie理想上左(θ,θ)-导子的性质,得到如下结论:设R是2-扭自由素环,Z(R)是R的中心,U是R的Lie理想,且U?Z(R),d是R上的左(θ,θ)-导子,则d=0。Ring theory is an important part of algebra.Derivation theory is an important research content of operator algebra.It has always been a hot research topic to explore the structure of different rings through the properties of derivation on rings.With the continuous development of ring theory,the derivations on rings have been enriched and expanded,and many derived derivation have appeared successively,such as generalized derivation,left derivation,generalized(θ,θ)-derivation,left(θ,θ)-derivation and so on.This paper takes the definition of left(θ,θ)-derivation as the breakthrough point,the properties of the left(θ,θ)-derivation on Lie ideal of 2-torsion free prime ring are discussed by the substitution method.The conclusion is as follows:Let R be a 2-torsion free prime ring with center Z(R),U a Lie Ideal of R and■,where d is the left(θ,θ)-derivation on R.Thend=0.

关 键 词：2-扭自由素环 LIE理想 导子 左(θ θ)-导子 

分 类 号：O153.3[理学—数学]