2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54631We study all possible $U(1)$-extensions of the standard model (SM) in the framework of noncommutative geometry (NCG) with the algebra $\hhh\op\cc\op\cc\op M_3(\cc)$. Comparison to experimental data about the mass of a hypothetical $Z'$ gauge boson leads to the necessity of introducing at least one new family of heavy fermions.16 pages, LaTexHigh Energy Physics - Theorytext