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 |
|---|---|
| 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 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
Cite this
}
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.
UR - http://www.scopus.com/inward/record.url?scp=84955489044&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84955489044&partnerID=8YFLogxK
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 -