Counting non-isomorphic generalized Hamilton quaternions

Year 2022, Volume: 31 Issue: 31, 143 - 160, 17.01.2022

Jose Maria Grau Celino Mıguel Antonio M. Oller-marcen

https://doi.org/10.24330/ieja.1058426

Abstract

In this paper we study the isomorphisms of generalized Hamilton quaternions $\Big(\frac{a,b}{R}\Big)$ where $R$ is a finite unital commutative ring of odd characteristic and $a,b \in R$. We obtain the number of non-isomorphic classes of generalized Hamilton quaternions in the case where $R$ is a principal ideal ring. This extends the case $R=\mathbb{Z}/n\mathbb{Z}$
where $n$ is an odd integer.

Keywords

Finite local ring , quaternion algebra , Hensel lemma

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