On (m,n)-Derivations of Some Algebras
On (m,n)-Derivations of Some Algebras
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DOI：
10.2478/dema-2014-0054
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发表时间：
2012-03
影响因子：
2
通讯作者：
Q. Shen;Jiankui Li;Jianbin Guo
中科院分区：
文献类型：
--
作者：
Q. Shen;Jiankui Li;Jianbin Guo
设A是单位代数，δ是A到其自身的线性映射，m，n是固定整数。我们称δ为Z处的(m，n)-可导映射，如果mδ(AB)+nδ(BA)=mδ(A)B+Maδ(B)+nδ(B)A对所有AB=Z的A，B∈A.本文刻画了广义矩阵代数上的IA⊕0，I)。我们还研究了CSL代数上的(m，n)-可导映射。揭示了这类映射与Lie导子、Jordan导子和导子之间的关系。
Abstract Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA ⊕ 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.