# Rings, Ideals, Quotient Rings in Sage

Hi everybody. I am new to sage. I want to construct rings, ideals, and quotient rings. I used Z.IntegerRing() to generate the ring of integers.

Question 1: Then I used I = Z.ideal(2) to get the ideal generated by 2 (even numbers). Question: How can I display the Elements. E.g. I(2) does not work in order to display the second element of the ideal.

Question 2: To generate the quotientring Z/2Z i used S = Z.quotient_ring(I). What if I want to generate the quotientring 2Z/6Z ? S = I.quotient_ring(J) does not work (I = Z.ideal(2), J = Z.ideal(6).

Thanks for any help

What is Z?

Z is my integer ring

Can you give it to me?

I think Z is defined as

`Z = IntegerRing()`

, not`Z.IntegerRing()`

.