How to multiple ideals in the ring of integers - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-19T02:36:28Z http://mathoverflow.net/feeds/question/50301 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/50301/how-to-multiple-ideals-in-the-ring-of-integers How to multiple ideals in the ring of integers PasGal 2010-12-24T19:17:58Z 2010-12-24T19:17:58Z <p>Hi! I have some problems with my university task: find the ideal class group in Z[$\sqrt{-89}$]</p> <p>I have found all ideals: $(1,\frac{3+i*\sqrt{89}}{7})$, $(1,\frac{1+i*\sqrt(89)}{18})$, etc. But the problem is to find out how do they multiply to each other For example, if I multiply $(1,\frac{3+i*\sqrt{89}}{7})$ to itself I have $(1,\frac{3+i*\sqrt{89}}{7},\frac{-80+2*i*\sqrt{89}}{49})$ but I really don't have any idea which element of my group this ideal is.</p>