Abstract
Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R → A is called strong commutativity preserving (SCP) on R if [f (x), f (y)] = [x, y] for all x, y ∈ R. In this paper we show that if f is SCP on R, then there exist λ ∈ C, λ2 = 1 and an additive map μ : R → Z (A) such that f (x) = λ x + μ (x) for all x ∈ R where C is the extended centroid of A, unless charA = 2 and A satisfies the standard identity of degree 4.
| Original language | English |
|---|---|
| Pages (from-to) | 1601-1609 |
| Number of pages | 9 |
| Journal | Linear Algebra and Its Applications |
| Volume | 428 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2008 Apr 1 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
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Strong commutativity preserving maps on Lie ideals. / Lin, Jer Shyong; Liu, Cheng-Kai.
In: Linear Algebra and Its Applications, Vol. 428, No. 7, 01.04.2008, p. 1601-1609.Research output: Contribution to journal › Article
TY - JOUR
T1 - Strong commutativity preserving maps on Lie ideals
AU - Lin, Jer Shyong
AU - Liu, Cheng-Kai
PY - 2008/4/1
Y1 - 2008/4/1
N2 - Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R → A is called strong commutativity preserving (SCP) on R if [f (x), f (y)] = [x, y] for all x, y ∈ R. In this paper we show that if f is SCP on R, then there exist λ ∈ C, λ2 = 1 and an additive map μ : R → Z (A) such that f (x) = λ x + μ (x) for all x ∈ R where C is the extended centroid of A, unless charA = 2 and A satisfies the standard identity of degree 4.
AB - Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R → A is called strong commutativity preserving (SCP) on R if [f (x), f (y)] = [x, y] for all x, y ∈ R. In this paper we show that if f is SCP on R, then there exist λ ∈ C, λ2 = 1 and an additive map μ : R → Z (A) such that f (x) = λ x + μ (x) for all x ∈ R where C is the extended centroid of A, unless charA = 2 and A satisfies the standard identity of degree 4.
UR - http://www.scopus.com/inward/record.url?scp=38849151577&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38849151577&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2007.10.006
DO - 10.1016/j.laa.2007.10.006
M3 - Article
AN - SCOPUS:38849151577
VL - 428
SP - 1601
EP - 1609
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
IS - 7
ER -