Centralizers and Pseudo-Degree Functions
This paper generalizes a proof of certain results by Hellström and Silvestrov (J Algebr 314:17–41, 2007, ) 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.
KeywordsOre extensions Algebraic dependence Commutative subrings
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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