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

  • José María Grau
  • Celino Miguel
  • Antonio M. Oller-MarcénEmail author


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 \(\Big (\frac{a,b}{\mathbb {Z}/n\mathbb {Z}}\Big )\).


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

Mathematics Subject Classification

11R52 16-99 


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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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