  In this paper we prove that the cyclotomic Khovanov-Lauda-Rouquier algebras
in type A, $\mathscr R_n^\Lambda$, are $\mathbb{Z}$-free. We then extend the
graded cellular basis of $\mathscr R_n^\Lambda$ constructed by Hu and Mathas to
$\mathscr R_n$ and use this basis to give a classification of all irreducible
$\mathscr R_n$-modules.
