Book on ideal theory in Hurwitz quaternions - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T01:28:40Z http://mathoverflow.net/feeds/question/104403 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104403/book-on-ideal-theory-in-hurwitz-quaternions Book on ideal theory in Hurwitz quaternions Anton 2012-08-10T11:20:39Z 2012-08-11T00:28:22Z <p>Hello,</p> <p>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 $\mathcal{O}(\mu)$.</p> <p>Finally, I'd be glad if you recomend me some articles that study the problem of solving the equation of the form</p> <p>$$\rho\mu = \mu'\rho$$</p> <p>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> <p>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.</p> http://mathoverflow.net/questions/104403/book-on-ideal-theory-in-hurwitz-quaternions/104429#104429 Answer by PaPiro for Book on ideal theory in Hurwitz quaternions PaPiro 2012-08-10T18:34:27Z 2012-08-11T00:28:22Z <p>In response to your first question (a book that studies the set of HQ), there is a book from Hurwitz, in German, <em>Vorlesungen über die Zahlentheorie der Quaternionen</em>, Verlag von Julius Springer, 1919, available <a href="http://archive.org/stream/vorlesungenber00hurwuoft#page/n3/mode/2up" rel="nofollow">here</a></p>