Could someone help me find the complete list of ideals for the ring Z x Z?
Thanks.
Since, $\displaystyle \mathbb{Z}$ is cyclic all subgroups must have form $\displaystyle n\mathbb{Z}$.
We note that $\displaystyle n\mathbb{Z}$ and $\displaystyle m\mathbb{Z}$ are subgroups of $\displaystyle \mathbb{Z}$ thus, $\displaystyle n\mathbb{Z} \times m\mathbb{Z}$ is an additive subgroup of $\displaystyle \mathbb{Z}\times \mathbb{Z}$ which is also an ideal.