It is a well-known fact $SL(n,\mathbb Z)$ a lattice in $SL(n,\mathbb R)$. The definition of an irreducible lattice can be found in the following Wikipedia link:
https://en.m.wikipedia.org/wiki/Lattice_(discrete_subgroup)#Irreducibility
I wonder how to show that $SL(n,\mathbb Z)$ is indeed an irreducible lattice $SL(n,\mathbb R)$. Namely the intersection of $SL(n,\mathbb Z)$ with any factor of $SL(n,\mathbb R)$ is either dense (unlikely I think) or not a lattice.