Quantum function algebras as quantum enveloping algebras

Inspired by a result in [F. Gavarini, "Quantization of Poisson groups", Pacific Journal of Mathematics 186 (1998), 217-266], we locate three integer forms of F_q[SL(n+1)] over the ring of Laurent polynomials in q, with a presentation by generators and relations, which for q=1 specialize to U(h), where h is the Lie bialgebra of the Poisson Lie group dual SL(n+1). In sight of this, we prove also two PBW-like theorems for F_q[SL(n+1)], both related to the classical PBW theorem for U(h).