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We introduce higher-rank analogues of the Leavitt path algebras, which we call the Kumjian-Pask algebras. We prove graded and Cuntz-Krieger uniqueness theorems for these algebras, and analyze their ideal structure.doi:10.1090/s0002-9947-2013-05717-0 fatcat:nui5xezrhnbm3if2agtvaoridq