2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76511With the help of the multigraded Nijenhuis-- Richardson bracket and the multigraded Gerstenhaber bracket from [7] for every $n\ge 2$ we define $n$-ary associative algebras and their modules and also $n$-ary Lie algebras and their modules, and we give the relevant formulas for Hochschild and Chevalley cohomogy.18 pages, AmSTeXQuantum Algebra08A62, 16B99, 17B99text