  We provide an alternative approach to the Faddeev-Reshetikhin-Takhtajan
presentation of the quantum group U_q(g), with L-operators as generators and
relations ruled by an R-matrix. We look at U_q(g) as being generated by the
quantum Borel subalgebras U_q(b_+) and U_q(b_-), and we use the standard
presentation of the latters as quantum function algebras. When g = gl(n) these
Borel quantum function algebras are generated by the entries of a triangular
q-matrix, thus eventually U_q(gl(n)) is generated by the entries of an upper
triangular and a lower triangular q-matrix, which share the same diagonal. The
same elements generate over the ring of Laurent polynomials the unrestricted
integer form of U_q(gl(n)) of De Concini and Procesi, which we present
explicitly, together with a neat description of the associated quantum
Frobenius morphisms at roots of 1. All this holds, mutatis mutandis, for g =
sl(n) too.
