2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64417We generalize results of Mingo and Nica on graded independence from the context of $\mathbb Z_2$--graded (Fermionic) noncommutative probability spaces to that of $\mathbb Z_n$--graded noncommutative probability spaces. We show that for $q$ a primitive $n$-th root of unity, the $q$-cumulants defined by Nica linearize the addition of homogeneous $\mathbb Z_n$--graded independent random variables.16 pages, Latex. Minor revisionOperator AlgebrasProbability46L53text