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Centralizers and Pseudo-Degree Functions

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Engineering Mathematics II

Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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References

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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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Authors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Box 883, 721 23, Västerås, Sweden

    Johan Richter

Authors
  1. Johan Richter
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Correspondence to Johan Richter .

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Editors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University,, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics,, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Richter, J. (2016). Centralizers and Pseudo-Degree Functions. In: Silvestrov, S., Rančić, M. (eds) Engineering Mathematics II. Springer Proceedings in Mathematics & Statistics, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-319-42105-6_5

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