MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am looking for a book that studies the set of Hurwitz quaternions (HQ). In particular, I am interested in a connection between HQ and imaginary quadratic fields (IQF); quaternion orders $\mathcal{O}(\mu)$ and ideals of the form $n[a, b + \mu]$; information on similarities and differences between ideal theory in IQF and HQ, as well as some info about the algorithms on how to perform multiplication and reduction of ideals in $\mathcal{O}(\mu)$.

Finally, I'd be glad if you recomend me some articles that study the problem of solving the equation of the form

$$ \rho\mu = \mu'\rho $$

for $\rho$. This equation allows us to "move" an ideal $n[a,b+\mu]$ with generator $\rho$ from order $\mathcal{O}(\mu)$ to order $\mathcal{O}(\mu')$. Also, if you know articles that study ambiguous ideals in HQ, I'd be glad to read them.

P.S. The only article that I am aware of is B. Venkov's "On Quaternion Arithmetic" which is pretty old (1929). I believe there exist more up-to-date articles.

share|cite|improve this question

In response to your first question (a book that studies the set of HQ), there is a book from Hurwitz, in German, Vorlesungen über die Zahlentheorie der Quaternionen, Verlag von Julius Springer, 1919, available here

share|cite|improve this answer
up vote 1 down vote accepted

I feel bad for answering my own question, but after studying a topic for a while, my explorations resulted in a research paper, which answers all of the questions above.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.