2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113966We develop a new method to deal with the Cancellation Conjecture of Zariski in different environments. We prove the conjecture for free associative algebras of rank two. We also produce a new proof of the conjecture for polynomial algebras of rank two over fields of zero characteristic.Rings and AlgebrasCommutative AlgebraPrimary 16S10. Secondary 13B10, 13F20, 14R10, 16W20text