@article{article_1058426, title={Counting non-isomorphic generalized Hamilton quaternions}, journal={International Electronic Journal of Algebra}, volume={31}, pages={143–160}, year={2022}, DOI={10.24330/ieja.1058426}, author={Grau, Jose Maria and Mıguel, Celino and Oller-marcen, Antonio M.}, keywords={Finite local ring, quaternion algebra, Hensel lemma}, 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.}, number={31}, publisher={Abdullah HARMANCI}