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Centralizers and Pseudo-Degree Functions

  • Johan RichterEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 179)

Abstract

This paper generalizes a proof of certain results by Hellström and Silvestrov (J Algebr 314:17–41, 2007, [8]) on centralizers in graded algebras. We study centralizers in certain algebras with valuations. We prove that the centralizer of an element in these algebras is a free module over a certain ring. Under further assumptions we obtain that the centralizer is also commutative.

Keywords

Ore extensions Algebraic dependence Commutative subrings 

Notes

Acknowledgement

This work was performed in part while the author was employed at Lund University and in part while the author was employed at Mälardalen University.

The author wishes to thank Lars Hellström and Johan Öinert for helpful discussions.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Division of Applied Mathematics, School of EducationCulture and Communication, Mälardalen UniversityVästeråsSweden

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