Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Mohammad Ashraf; Nazia Parveen; Bilal Ahmad Wani

Communications in Mathematics (2017)

  • Volume: 25, Issue: 1, page 35-53
  • ISSN: 1804-1388

Abstract

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Let 𝔄 = 𝒜 be the triangular algebra consisting of unital algebras 𝒜 and over a commutative ring R with identity 1 and be a unital ( 𝒜 , ) -bimodule. An additive subgroup 𝔏 of 𝔄 is said to be a Lie ideal of 𝔄 if [ 𝔏 , 𝔄 ] 𝔏 . A non-central square closed Lie ideal 𝔏 of 𝔄 is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on 𝔄 , every generalized Jordan triple higher derivation of 𝔏 into 𝔄 is a generalized higher derivation of 𝔏 into 𝔄 .

How to cite

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Ashraf, Mohammad, Parveen, Nazia, and Wani, Bilal Ahmad. "Generalized Higher Derivations on Lie Ideals of Triangular Algebras." Communications in Mathematics 25.1 (2017): 35-53. <http://eudml.org/doc/294132>.

@article{Ashraf2017,
abstract = {Let $\mathfrak \{A\} = \begin\{pmatrix\}\mathcal \{A\} & \mathcal \{M\}\\ &\mathcal \{B\} \end\{pmatrix\}$ be the triangular algebra consisting of unital algebras $\mathcal \{A\}$ and $\mathcal \{B\}$ over a commutative ring $R$ with identity $1$ and $ \mathcal \{M\}$ be a unital $ \mathcal \{(A, B)\}$-bimodule. An additive subgroup $ \mathfrak \{ L \}$ of $ \mathfrak \{ A \} $ is said to be a Lie ideal of $\mathfrak \{A\}$ if $[\mathfrak \{L\},\mathfrak \{A\}]\subseteq \mathfrak \{L\}$. A non-central square closed Lie ideal $\mathfrak \{ L \}$ of $\mathfrak \{ A \}$ is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on $\mathfrak \{A\}$, every generalized Jordan triple higher derivation of $ \mathfrak \{L\}$ into $\mathfrak \{A\}$ is a generalized higher derivation of $ \mathfrak \{L\}$ into $ \mathfrak \{ A \}$.},
author = {Ashraf, Mohammad, Parveen, Nazia, Wani, Bilal Ahmad},
journal = {Communications in Mathematics},
keywords = {Admissible Lie Ideals; triangular algebra; generalized higher derivation; generalized Jordan higher derivation; generalized Jordan triple higher derivation},
language = {eng},
number = {1},
pages = {35-53},
publisher = {University of Ostrava},
title = {Generalized Higher Derivations on Lie Ideals of Triangular Algebras},
url = {http://eudml.org/doc/294132},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Ashraf, Mohammad
AU - Parveen, Nazia
AU - Wani, Bilal Ahmad
TI - Generalized Higher Derivations on Lie Ideals of Triangular Algebras
JO - Communications in Mathematics
PY - 2017
PB - University of Ostrava
VL - 25
IS - 1
SP - 35
EP - 53
AB - Let $\mathfrak {A} = \begin{pmatrix}\mathcal {A} & \mathcal {M}\\ &\mathcal {B} \end{pmatrix}$ be the triangular algebra consisting of unital algebras $\mathcal {A}$ and $\mathcal {B}$ over a commutative ring $R$ with identity $1$ and $ \mathcal {M}$ be a unital $ \mathcal {(A, B)}$-bimodule. An additive subgroup $ \mathfrak { L }$ of $ \mathfrak { A } $ is said to be a Lie ideal of $\mathfrak {A}$ if $[\mathfrak {L},\mathfrak {A}]\subseteq \mathfrak {L}$. A non-central square closed Lie ideal $\mathfrak { L }$ of $\mathfrak { A }$ is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on $\mathfrak {A}$, every generalized Jordan triple higher derivation of $ \mathfrak {L}$ into $\mathfrak {A}$ is a generalized higher derivation of $ \mathfrak {L}$ into $ \mathfrak { A }$.
LA - eng
KW - Admissible Lie Ideals; triangular algebra; generalized higher derivation; generalized Jordan higher derivation; generalized Jordan triple higher derivation
UR - http://eudml.org/doc/294132
ER -

References

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