可换环上全矩阵代数的若当导子和局部若当导子(英文)  

Jordan Derivations and Local Jordan Derivations on Full Matrix Algebras over Commutative Rings

作　　者：赵延霞[1] 

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《南开大学学报（自然科学版）》2014年第6期98-104,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by National Natural Science Foundation of China(11126121);Doctor Foundation of Henan Polytechnic University(B2010-93);Natural Science Research Program of Science and Technology Department of Henan Province(112300410120);Natural Science Research Program of Education Department of Henan Province(2011B110016);Applied Mathematics Provincial-level Key Discipline of Henan Province

摘　　要：令R表示含单位元1的可换环,2是R的可逆元,Mn(R)表示由R上所有n×n阶阵形成的代数.证明了Mn(R)的每一个若当导子是内导子,每一个局部若当导子是内导子.作为应用,证明了Mn(R)的每一个局部导子是内导子.Let Rbe a commutative ring with identity 1and unit 2,Mn（R）the algebra consisting of all nby n matrices over R.It is proved that every Jordan derivation of Mn（R）is an inner derivation and that every local Jordan derivation of Mn（R）is an inner derivation.As an application,we show that every local derivation of Mn（R）is proved be inner.

关 键 词：若当导子 局部若当导子 全矩阵代数 局部导子 可换环 

分 类 号：O151[理学—数学]