三角代数上的导子  

Derivations of Triangular Algebra

作　　者：马晶[1] 罗志君 李霞[1] MA Jing;LUO Zhijun;LI Xia(College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2018年第5期1041-1044,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:J1310022;11771176)

摘　　要：设R是有单位元的交换环,A,B是R上的单式代数,M是非零(A,B)-单式双模,且作为A,B-模都是忠实的.记T=(A M0B)={(a m0b)a∈A,b∈B,m∈}M为A,B,M构成的三角代数.利用三角代数T上导子的性质,给出T上分别满足广义恒等式D([X,Y])=k[X,Y]和D([X,Y])=k[D(X),Y]的导子结构,以及满足广义恒等式D(X。Y)=kX。Y和D(X。Y)=kD(X)。Y的导子结构,其中k为R中单位.Let Rbe a commutative ring with unit elements,A,Bbe unitary algebras over Rand M be nonzero(A,B)-bimodule which was faithful as a left A-module and also as a right B-module.Let T=(A M0B)={(a m0ba)∈A,b∈B,m∈ }M be a triangular algebra made up of A,B,M.Using the properties of derivations of triangular algebras T,we gave derivation structure satisfying the generalized identities D([X,Y])=k[X,Y]or D([X,Y])=k[D(X),Y]on T,respectively,as well as the derivation structure satisfying the generalized identities D(X。Y)=kX 。Y or D(X。Y)=kD(X)。Y,where kis a unit of R.

关 键 词：三角代数 导子 交换环 

分 类 号：O153.3[理学—数学]