Abstract
Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. 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. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M2(F), the 2 × 2 matrix ring over a field F.
Original language | English |
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Pages (from-to) | 898-911 |
Number of pages | 14 |
Journal | Communications in Algebra |
Volume | 44 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2016 Feb 1 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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Annihilators of Skew Derivations with Engel Conditions on Lie Ideals. / Chou, Ming Chu; Liu, Cheng-Kai.
In: Communications in Algebra, Vol. 44, No. 2, 01.02.2016, p. 898-911.Research output: Contribution to journal › Article
TY - JOUR
T1 - Annihilators of Skew Derivations with Engel Conditions on Lie Ideals
AU - Chou, Ming Chu
AU - Liu, Cheng-Kai
PY - 2016/2/1
Y1 - 2016/2/1
N2 - Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. 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. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M2(F), the 2 × 2 matrix ring over a field F.
AB - Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. 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. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M2(F), the 2 × 2 matrix ring over a field F.
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U2 - 10.1080/00927872.2014.990028
DO - 10.1080/00927872.2014.990028
M3 - Article
AN - SCOPUS:84955489044
VL - 44
SP - 898
EP - 911
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 2
ER -