Smallest Ideal in $M_2(Z)$

77 Views Asked by At

What is the smallest ideal in $M_2(Z)$ containing $\begin{pmatrix} 1 & 0 \\ 0 & 0\end{pmatrix}$? I'm a bit unsure about what "smallest" means here. I've found all of the ideals of $M_2(Z)$, however. Thank you in advance!