Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras
Let R be a commutative ring with identity element, A and B be unital algebras over R and let M be (A,B)-bimodule which is faithful as a left A-module and also faithful as a right B-module. Suppose that A = Tri(A,M,B) is a triangular algebra which is 2-torsion free and σ, Γ be automorphisms of A. A m...
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2018-05-01
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doaj-9904bde8d6ac4b7db342dff0e64428c52021-10-02T17:45:57ZengDe GruyterSpecial Matrices2300-74512018-05-016121622810.1515/spma-2017-0008spma-2017-0008Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebrasAlkenani Ahmad N.0Ashraf Mohammad1Jabeen Aisha2Department of Mathematics, King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh,202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh,202002, IndiaLet R be a commutative ring with identity element, A and B be unital algebras over R and let M be (A,B)-bimodule which is faithful as a left A-module and also faithful as a right B-module. Suppose that A = Tri(A,M,B) is a triangular algebra which is 2-torsion free and σ, Γ be automorphisms of A. A map δ:A→A (not necessarily linear) is called a multiplicative generalized (σ, Γ)-derivation (resp. multiplicative generalized Jordan (σ, Γ)-derivation) on A associated with a (σ, Γ)-derivation (resp. Jordan (σ, Γ)-derivation) d on A if δ(xy) = δ(x)r(y) + σ(x)d(y) (resp. σ(x<sup>2</sup>) = δ(x)r(x) + δ(x)d(x)) holds for all x, y Є A. In the present paper it is shown that if δ:A→A is a multiplicative generalized Jordan (σ, Γ)-derivation on A, then δ is an additive generalized (σ, Γ)-derivation on A.https://doi.org/10.1515/spma-2017-0008triangular algebrageneralized jordan (σγ)-derivationgeneralized (σγ)-derivation16w2515a78 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Alkenani Ahmad N. Ashraf Mohammad Jabeen Aisha |
spellingShingle |
Alkenani Ahmad N. Ashraf Mohammad Jabeen Aisha Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras Special Matrices triangular algebra generalized jordan (σ γ)-derivation generalized (σ γ)-derivation 16w25 15a78 |
author_facet |
Alkenani Ahmad N. Ashraf Mohammad Jabeen Aisha |
author_sort |
Alkenani Ahmad N. |
title |
Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras |
title_short |
Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras |
title_full |
Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras |
title_fullStr |
Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras |
title_full_unstemmed |
Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras |
title_sort |
nonlinear generalized jordan (σ, γ)-derivations on triangular algebras |
publisher |
De Gruyter |
series |
Special Matrices |
issn |
2300-7451 |
publishDate |
2018-05-01 |
description |
Let R be a commutative ring with identity element, A and B be unital algebras over R and let M be (A,B)-bimodule which is faithful as a left A-module and also faithful as a right B-module. Suppose that A = Tri(A,M,B) is a triangular algebra which is 2-torsion free and σ, Γ be automorphisms of A. A map δ:A→A (not necessarily linear) is called a multiplicative generalized (σ, Γ)-derivation (resp. multiplicative generalized Jordan (σ, Γ)-derivation) on A associated with a (σ, Γ)-derivation (resp. Jordan (σ, Γ)-derivation) d on A if δ(xy) = δ(x)r(y) + σ(x)d(y) (resp. σ(x<sup>2</sup>) = δ(x)r(x) + δ(x)d(x)) holds for all x, y Є A. In the present paper it is shown that if δ:A→A is a multiplicative generalized Jordan (σ, Γ)-derivation on A, then δ is an additive generalized (σ, Γ)-derivation on A. |
topic |
triangular algebra generalized jordan (σ γ)-derivation generalized (σ γ)-derivation 16w25 15a78 |
url |
https://doi.org/10.1515/spma-2017-0008 |
work_keys_str_mv |
AT alkenaniahmadn nonlineargeneralizedjordansgderivationsontriangularalgebras AT ashrafmohammad nonlineargeneralizedjordansgderivationsontriangularalgebras AT jabeenaisha nonlineargeneralizedjordansgderivationsontriangularalgebras |
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1716850561942290432 |