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Generalized Quaternion Rings over \(\mathbb {Z}/n\mathbb {Z}\) for an Odd \(\varvec{n}\)

  • José María Grau
  • Celino Miguel
  • Antonio M. Oller-Marcén
Article
  • 62 Downloads

Abstract

We consider a generalization of the quaternion ring \(\Big (\frac{a,b}{R}\Big )\) over a commutative unital ring R that includes the case when a and b are not units of R. In this paper, we focus on the case \(R=\mathbb {Z}/n\mathbb {Z}\) for and odd n. In particular, for every odd integer n we compute the number of non R-isomorphic generalized quaternion rings \(\Big (\frac{a,b}{\mathbb {Z}/n\mathbb {Z}}\Big )\).

Keywords

Quaternion algebra \(\mathbb {Z}/n\mathbb {Z}\) Structure 

Mathematics Subject Classification

11R52 16-99 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad de OviedoOviedoSpain
  2. 2.Instituto de TelecomunicaçoesUniversidade de Beira InteriorPolo de CovilhaPortugal
  3. 3.Centro Universitario de la Defensa de ZaragozaSaragossaSpain

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