Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of Type A

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In this paper we prove that the cyclotomic Khovanov-Lauda-Rouquier algebras in type A, RₙΛ, are Z-free. We then extend the graded cellular basis of RₙΛ constructed by Hu and Mathas to Rₙ and use this basis to give a classification of all irreducible Rₙ-modules.