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|Title: ||An Engel Condition with Skew Derivations|
|Authors: ||Chou, Ming-Chu;Liu, Cheng-Kai|
|Keywords: ||Prime ring;Lie ideal;Automorphism;Skew derivation;Generalized polynomial identity (GPI)|
|Issue Date: ||2013-01-07T01:43:54Z
|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:||[數學系] 期刊論文|
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