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.
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
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
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
Jordan derivation
local Jordan derivation
full matrix algebra
local derivation
commutative ring
