Kragujevac Journal of Mathematics, Volume (43), No (2), Year (2019-6) , Pages (267-273)

Title : ( INNER HIGHER DERIVATIONS ON ALGEBRAS )

Authors: elham tafazzoli , Madjid Mirzavaziri ,

Citation: BibTeX | EndNote

Abstract

Let A be an algebra. A sequence d = {dn}∞ n=0 of linear operators on A is called a higher derivation if d0 is the identity mapping on A and dn(xy) = Pn k=0 dk(x)dn−k(y), for each n = 0, 1, 2, . . . and x, y ∈ A. We say that a higher derivation d is inner if there is a sequence a = {an}∞ n=1 in A such that (n + 1)dn+1(x) = Pn k=0 ak+1dn−k(x) − dn−k(x)ak+1, for each n = 0, 1, 2, . . . and x ∈ A. Giving a characterization for inner higher derivations on a torsion free algebra A, we show that each higher derivation on A is inner provided that each derivation on A is inner.

Keywords

, Derivation, inner derivation, higher derivation, inner higher derivation
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@article{paperid:1076531,
author = {Tafazzoli, Elham and Mirzavaziri, Madjid},
title = {INNER HIGHER DERIVATIONS ON ALGEBRAS},
journal = {Kragujevac Journal of Mathematics},
year = {2019},
volume = {43},
number = {2},
month = {June},
issn = {1450-9628},
pages = {267--273},
numpages = {6},
keywords = {Derivation; inner derivation; higher derivation; inner higher derivation},
}

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%0 Journal Article
%T INNER HIGHER DERIVATIONS ON ALGEBRAS
%A Tafazzoli, Elham
%A Mirzavaziri, Madjid
%J Kragujevac Journal of Mathematics
%@ 1450-9628
%D 2019

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