What exactly are the right ideals of $L=H(\mathbb Z)=\{\,a+bi+cj+dk;\quad a,b,c,d \in \mathbb Z\}$ (the Lipschitz quaternions)?
we can see here
Ideal class "group" of Lipschitz (fully-integer) quaternions
These are $(\alpha)$ , $(\alpha, \alpha\frac{1+i+j+k}{2})$. I am confused...Is it correct? I can't understand its proof!! How the last is possible? while $\frac{1}{2}\not\in\mathbb Z$!!
IS $(\alpha, \alpha\frac{1+i+j+k}{2})$is a subset of $L$ at all?