Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-4,
author = {Jan Krempa},
title = {On free subgroups of units in quaternion algebras II},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {29-32},
zbl = {1045.16015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-4}
}
Jan Krempa. On free subgroups of units in quaternion algebras II. Colloquium Mathematicae, Tome 96 (2003) pp. 29-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-4/