I have the non-commutative ring R which is

$\displaystyle

\left[

\begin{array}{ c c }

\mathbb Z & \mathbb Q \\

0 & \mathbb Q

\end{array} \right]

$

How can I show that every right ideal in the ring R is projective and finitely generated. And how can I use this to show that the right global dimension of R is 1.