Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D（x）x - xG（x） ∈ Z for all x ∈S. The main purpose of this paper is to describe the structur...Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D（x）x - xG（x） ∈ Z for all x ∈S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime ease is also considered.展开更多
Let R be a*-ring with the center Z(R)and N be the set of nonnegative integers.In this paper,it is shown that if R contains a nontrivial self-adjoint idempotent which admits a generalized Lie higher derivable mapping△...Let R be a*-ring with the center Z(R)and N be the set of nonnegative integers.In this paper,it is shown that if R contains a nontrivial self-adjoint idempotent which admits a generalized Lie higher derivable mapping△={G_(n)}_(n∈N)associated with a*-Lie higher derivable mapping L={L_(n)}_(n∈N),then for any X,Y in R and for each n in N there exists an element Z_(X,Y)(depending on X and Y)in the center Z(R)such that G_(n)(X+Y)=G_(n)(X)+G_(n)(Y)+Z_(X,Y).展开更多
In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanis...In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanishing at commuta-tors.展开更多
The additive （generalized） ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumptions, that an additive map L is an additive generalized Lie derivation if and only if it is ...The additive （generalized） ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumptions, that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive （generalized） E-Lie derivation with ξ -if and only if it is an additive （generalized） derivation satisfying L（ξA） =- ξL（A） for all A. These results are then used to characterize additive （generalized） ξ-Lie derivations on several operator Mgebras such as Banach space standard operator algebras and yon Neumman algebras.展开更多
Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A^2) = 2 mAδ(A) + 2nδ(A)A for every ...Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A^2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.展开更多
Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, t...Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.展开更多
文摘Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D（x）x - xG（x） ∈ Z for all x ∈S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime ease is also considered.
基金supported by the MATRICS research grant from DST(SERB)(no.MTR/2017/000033).
文摘Let R be a*-ring with the center Z(R)and N be the set of nonnegative integers.In this paper,it is shown that if R contains a nontrivial self-adjoint idempotent which admits a generalized Lie higher derivable mapping△={G_(n)}_(n∈N)associated with a*-Lie higher derivable mapping L={L_(n)}_(n∈N),then for any X,Y in R and for each n in N there exists an element Z_(X,Y)(depending on X and Y)in the center Z(R)such that G_(n)(X+Y)=G_(n)(X)+G_(n)(Y)+Z_(X,Y).
基金The first author is supported by Natural Science Foundation of Shandong Province,China(Grant No.ZR2015PA010)National.Natural Science Foundation of China(GrantNo.11526123)The third author is supported by the National Natural Science Foundation of China(Grant No.11401273).
文摘In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanishing at commuta-tors.
基金supported by National Natural Science Foundation of China(Grant No.11101250)Youth Foundation of Shanxi Province(Grant No.2012021004)+3 种基金 Young Talents Plan for Shanxi Universitysupported by National Natural Science Foundation of China(Grant No.11171249)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20101402110012)International Cooperation Program in Sciences and Technology of Shanxi Province(Grant No.2011081039)
文摘The additive （generalized） ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumptions, that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive （generalized） E-Lie derivation with ξ -if and only if it is an additive （generalized） derivation satisfying L（ξA） =- ξL（A） for all A. These results are then used to characterize additive （generalized） ξ-Lie derivations on several operator Mgebras such as Banach space standard operator algebras and yon Neumman algebras.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11801342 and 11801005)
文摘Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A^2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.
基金Supported by the National Natural Science Foundation of China(Grant No.11571247)supported by the union program of department of science technology in Guizhou province,Anshun government and Anshun university(Grant No.201304)
文摘Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.
