Hello, and thank you very much for reading.

Hate these kinds of questions:

Let p be a prime number.

Let R= Z(p) be the ring defined as followed:

Z(p) = {x/y : gcd(y,p)=1} (notice that it's not the ring {0,1,...,p-1}!)

I need to characterize all the ideals in this ring, and all of it's quotient rings...

I already proved Z(p) is a ring (I needed to do so before this question).

I also noticed that an element x/y is invertible if and only if x is

**not** in pZ (meaning, if and only if gcd(x,p)=1).

I know that if an Ideal cosist an invertible element then it is all of R, so I'm seeking for ideals that consist of elements x/y such that gcd(x,p)=1. However, I cannot see how to find how many ideals of this type there are, and moreover - how to show that there are no other types of ideals... :-\

I'll think of quotient rings after I find the ideals...

I'm too stuck on this one...

Thank you in advance.

Yours truely

Tomer.