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Gelfand–Kirillov dimension of differential difference algebras

Part of: Chain conditions, growth conditions, and other forms of finiteness Rings and algebras arising under various constructions

Published online by Cambridge University Press:  01 September 2014

Yang Zhang  and
Xiangui Zhao
Yang Zhang
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 email yang.zhang@umanitoba.ca
Xiangui Zhao
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 email xian.zhao@umanitoba.ca

Abstract

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Differential difference algebras, introduced by Mansfield and Szanto, arose naturally from differential difference equations. In this paper, we investigate the Gelfand–Kirillov dimension of differential difference algebras. We give a lower bound of the Gelfand–Kirillov dimension of a differential difference algebra and a sufficient condition under which the lower bound is reached; we also find an upper bound of this Gelfand–Kirillov dimension under some specific conditions and construct an example to show that this upper bound cannot be sharpened any further.

MSC classification

Secondary: 16P90: Growth rate, Gelfand-Kirillov dimension 16S36: Ordinary and skew polynomial rings and semigroup rings
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 485 - 495
Copyright
© The Author(s) 2014 

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