Ring detail

Name: Hurwitz quaternions

Description: $\left\{a+bi+cj+dk \in \mathbb{H} \mid a,b,c,d \in \mathbb{Z} \;\mbox{ or }\, a,b,c,d \in \mathbb{Z} + \tfrac{1}{2}\right\}$

Notes: Has a Euclidean division algorithm. Maximal order in the rational quaternions.

Keywords quaternion algebra subring


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  • Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    cardinality $\aleph_0$
    composition length left: $\infty$right: $\infty$
    global dimension left: 1right: 1
    Name Description
    Idempotents $\{0,1\}$
    Nilpotents $\{0\}$
    Zero divisors $\{0\}$