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Abstract

Let $A\subseteq {\mathbb Q}$ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra ${\rm H}(A)$ to units of certain rings of generalized quaternions ${\rm H}(A,a,b)=\left ({-a,-b\over A}\right ),$ where $a,b\in A.$ Next we show that there is an algebra embedding of the ring ${\rm H}(A,a,b)$ into the algebra of standard Cayley numbers over $A.$ Using this embedding we answer a question asked in the first part of this paper.