2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59717This is a first of our papers devoted to "noncommutative topology and graph theory". Its origin is the paper math.QA/0002238 by I. Gelfand, V. Retakh, and R.L. Wilson where a new class of noncommutative algebras $Q_n$ was introduced. The algebra $Q_n$ is closely related to factorizations of a generic polynomial of degree $n$ over a division algebra into linear factors.6 pages; amstexQuantum Algebra16W30, 15A15, 05E05text