Affiliation:
1. Department of Engineering, University of Messina, 98166 Messina, Italy
2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China
Abstract
Let [Formula: see text] be a prime ring of characteristic different from [Formula: see text], [Formula: see text] be its right Martindale quotient ring and [Formula: see text] be its extended centroid, [Formula: see text] be an automorphism of [Formula: see text], [Formula: see text] be a skew derivation of [Formula: see text] with associated automorphism [Formula: see text], [Formula: see text] and [Formula: see text] be two nonzero [Formula: see text]-generalized skew derivation of [Formula: see text] with associated term [Formula: see text] and [Formula: see text], respectively, [Formula: see text] be the set of the evaluations of [Formula: see text] on [Formula: see text], where [Formula: see text] is a non-central multilinear polynomial over [Formula: see text] in [Formula: see text] non-commuting variables. Let [Formula: see text] be such that [Formula: see text] for all [Formula: see text]. Then one of the following statements holds: (a) [Formula: see text] is central valued on [Formula: see text] and there exist [Formula: see text] such that [Formula: see text], [Formula: see text] for any [Formula: see text] with [Formula: see text]; (b) [Formula: see text] and [Formula: see text]. In the last part of the paper, we present some applications on the basis of the foregoing proposed result.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory