【摘要】 设R是任意含单位元的交换环,N(R)为R上(n+1)×(n+1)严格上三角矩阵构成的代数．本文证明了当n≥3且2是R的单位时,N(R)上任意Lie导子D可以唯一的表示为D=D_d+D_b+D_c+D_x,其中D_d,D_b,D_c,D_x分别是N(R)上的对角,极端,中心和内Lie导子,在n=2的情况,我们也证明了N(R)上任意Lie导子D可以表示为对角,极端,内Lie导子的和。更多还原

【Abstract】 Let R be an arbitrary commutative ring with identity.Denote by N(R) the algebra over R consisting of all strictly upper triangular (n+1)×(n+1) matrices over R.We prove that any Lie derivation D of N(R) can be uniquely expressed as D=D_d+D_b+D_c+D_x,where D_d,D_b,D_c,D_x are diagonal,extremal,central and inner Lie derivations,respectively,of N(R) when n(?)3 and R contains 2 as a unit.In the case n=2,we also prove that any Lie derivation D of N(R) can be expressed as a sum of diagonal,extremal and inner Lie derivations.更多还原