## How to multiple ideals in the ring of integers [closed]

Hi! I have some problems with my university task: find the ideal class group in Z[$\sqrt{-89}$]

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.

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How is $\frac{3+i*\sqrt{89}}{7}$ is $\mathbb Z[\sqrt{-89}]$? – Mariano Suárez-Alvarez Dec 24 2010 at 19:24
You mean fractional ideals, I guess... – Mariano Suárez-Alvarez Dec 24 2010 at 19:26
Yes, Z($\sqrt{-89}$) – PasGal Dec 24 2010 at 19:30
Voted to close because it is a homework problem. – Mark Sapir Dec 24 2010 at 19:34
@PasGal: I am not sure that the instructor who gave you this problem wanted you to use Google or MO. I suspect that (s)he prefers that you do it by yourself. If you have difficulty solving the problem, ask the instructor. – Mark Sapir Dec 24 2010 at 19:48