2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58778This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and differential polynomials. Such algebras posses a natural derivation and give us a new understanding of a nature of noncommutative symmetric functions.30 pages, last revisionQuantum Algebra16W30, 15A15, 05E05text