Counting non-isomorphic generalized Hamilton quaternions

Authors : Jose Maria GRAU, Celino MIGUEL, Antonio M OLLERMARCEN

Pages : 143-160

Doi:10.24330/ieja.1058426

View : 15 | Download : 6

Publication Date : 2022-01-17

Article Type : Research Paper

Abstract :In this paper we study the isomorphisms of generalized Hamilton quaternions $\Biginsert ignore into journalissuearticles values(\frac{a,b}{R}\Big);$ 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