2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61477A quantum solvable algebra is an iterated $q$-skew extension of a commutative algebra. We get finite statification of prime spectrum for quantum solvable algebras obeying some natural conditions. We prove that for any prime ideal $I$ the skew field of fractions $Fract(R/I)$ is isomorphic to the skew field of fractions of an algebra of twisted polynomials (Quantum Gel'fand-Kirillov Conjecture).Latex, 22pQuantum AlgebraRings and Algebras17B37, 16W35text