2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77120For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.10 pages, Uses AMS-LaTeX and XYpicRings and Algebras17A42; 16N34; 20N15On the $n$-ary algebras, semigroups and their universal coverstext