Algebraic skew derivations
Journal
Journal of Algebra
Journal Volume
353
Journal Issue
1
Pages
174-186
Date Issued
2012
Author(s)
Chuang, C.-L.
Abstract
Let R be a prime ring, C its extended centroid and RF (resp. Q) its left (resp. symmetric) Martindale quotient ring. Let δ be a σ-derivation of R, where σ is an automorphism of R. We show the equivalence of K-polynomials (resp. K-identities) of δ and cv-polynomials (resp. semi-invariant polynomials) in the Ore extension Q[X;σ, δ]. We prove the existence of K-polynomials of δ in certain rather general family of maps. As applications, the following are proved among other things: Consider the expression φ(x):=∑ i=0 na iδ i(x), where a i∈R F and a n≠0. (1) If dim Cφ(R)C<∞ then either R is a GPI-ring or φ(x)=0 for all x∈R F. (2) If φ(R)⊆C then either R is commutative or φ(x)=0 for all x∈R F. © 2011 Elsevier Inc.
Type
journal article