On generalized Lie derivations of Lie ideals of prime algebras

Ping Bao Liao; Cheng Kai Liu

doi:10.1016/j.laa.2008.10.022

On generalized Lie derivations of Lie ideals of prime algebras

Ping Bao Liao, Cheng Kai Liu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

Original language	English
Pages (from-to)	1236-1242
Number of pages	7
Journal	Linear Algebra and Its Applications
Volume	430
Issue number	4
DOIs	https://doi.org/10.1016/j.laa.2008.10.022
Publication status	Published - 2009 Feb 1

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2008.10.022

Fingerprint Dive into the research topics of 'On generalized Lie derivations of Lie ideals of prime algebras'. Together they form a unique fingerprint.

Cite this

@article{c47e197c49fa442d96d6c86eeb6dbf6f,

title = "On generalized Lie derivations of Lie ideals of prime algebras",

abstract = "Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.",

author = "Liao, {Ping Bao} and Liu, {Cheng Kai}",

year = "2009",

month = feb,

day = "1",

doi = "10.1016/j.laa.2008.10.022",

language = "English",

volume = "430",

pages = "1236--1242",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "4",

}

TY - JOUR

T1 - On generalized Lie derivations of Lie ideals of prime algebras

AU - Liao, Ping Bao

AU - Liu, Cheng Kai

PY - 2009/2/1

Y1 - 2009/2/1

N2 - Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

AB - Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

UR - http://www.scopus.com/inward/record.url?scp=58049192816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049192816&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2008.10.022

DO - 10.1016/j.laa.2008.10.022

M3 - Article

AN - SCOPUS:58049192816

VL - 430

SP - 1236

EP - 1242

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 4

ER -