Generalized Higher Derivations on Lie Ideals of Triangular Algebras

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 -