National Changhua University of Education Institutional Repository : Item 987654321/15015

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NCUEIR > College of Science > math > Periodical Articles > Item 987654321/15015

Please use this identifier to cite or link to this item: http://ir.ncue.edu.tw/ir/handle/987654321/15015

Title:	An Engel Condition with Skew Derivations
Authors:	Chou, Ming-Chu;Liu, Cheng-Kai
Contributors:	數學系
Keywords:	Prime ring;Lie ideal;Automorphism;Skew derivation;Generalized polynomial identity (GPI)
Date:	2009-11
Issue Date:	2013-01-07T01:43:54Z
Publisher:	SpringerLink
Abstract:	Let R be a prime ring and set [x, y]1 = [x, y] = xy − yx for x, y ∈ R and inductively [x, y]k = [[x, y]k−1, y] for k > 1.We apply the theory of generalized polynomial identitieswith automorphisms and skewderivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and R ⊆ M2(F) for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.
Relation:	Monatshefte fur Mathematik, 158(3): 259-270
Appears in Collections:	[math] Periodical Articles

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