2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231059It is shown that for every splitting of a polynomial with noncommutative coefficients into linear factors $(X-a_{k})$ with $a_{k}$'s commuting with coefficients, any cyclic permutation of linear factors gives the same result and all $a_{k}$ are roots of that polynomial. Examples are given and analyzed from Galois theory point of view.An example analyzed in more detail, grant number correctedQuantum AlgebraRings and Algebras13P05; 16U80; 15A30text