Stratification of prime spectrum of quantum solvable algebras

A 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).