Ideal of a ring

Ideal of a ring

I'm trying to describe an ideal of the ring $R=\left\{ \begin{pmatrix}a &
b\\ 0 & c \end{pmatrix}:a,b,c \in \mathbb{R}\right\} $
It's easy to prove that $I=\left\{ \begin{pmatrix}0 & a\\ 0 & 0
\end{pmatrix}:a\in\mathbb{R}\right\} $ and $J=\left\{ \begin{pmatrix}a &
b\\ 0 & 0 \end{pmatrix}:a,b\in\mathbb{R}\right\} $ are ideals of $R$
My question is: how can I find other ideals?
Any help would be appreciated.
Thanks.