算子代数上(m,n)-Jordan导子的刻画

设R是一个环,M是一个R-双边模,m和n是两个非负整数满足m+n≠0,如果δ是一个从R到M的可加映射满足对任意A∈R,(m+n)δ(A~2)=2mAδ(A)+2nδ(A)A,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个由R中幂等元代数生成的左(右)分离集,那么,当m,n0且m≠n时,每一个从R到M的(m,n)-Jordan导子恒等于零.还证明了,如果A和B是两个单位环,M是一个忠实的单位(A,B)-双边模(N是一个忠实的单位(B,A)-双边模),m,n0且m≠n,U=A N M B]是一个|mn(m-n)(m+n)|-无挠的广义矩阵环,那么每一个从U到自身的(m,n)-Jordan导子恒等于零.

Characterizations of(m,n)-Jordan Derivations on Operator Algebras

Let R be a ring, M be an R-bimodule, m and n be two fixed nonnegative integers with m+n=0.If an additive mapping δ from R into M satisfies(m+n)δ(A²)=2mAδ(A)+2nδ(A)A for every A in R, then δ is called an(m, n)-Jordan derivation.In this paper, we prove that if R is a unital ring and M is a unital Rbimodule with a left(right) separating set generated algebraically by all idempotents in R, then every(m, n)-Jordan derivation from R into M is identical with zero whenever m, n>0 and m=n.We also show that if A and B be two unital rings, M is a faithful unital(A, B)-bimodule(N is a faithful unital(B, A)-bimodule), m, n>0 and m=n, U=_N^A_B^M] is a |mn(m-n)(m+n)|-torsion-free generalized matrix ring, then every(m, n)-Jordan derivation from U into itself is equal to zero.