  Let ${\mathfrak g}$ be a finite dimensional complex simple Lie algebra, and
let $r,s\in \mathbb{C}^{\ast}$ be transcendental over $\mathbb{Q}$ such that
$r^{m}s^{n}=1$ implies $m=n=0$. We will obtain some basic properties of the
two-parameter quantized enveloping algebra $U_{r,s}^{+}(\mathfrak g)$. In
particular, we will verify that the algebra $U_{r,s}^{+}(\mathfrak g)$
satisfies many nice properties such as having normal separation, catenarity and
Dixmier-Moeglin equivalence. We shall study a concrete example, the algebra
$U_{r,s}^{+}(B_{2})$ in detail. We will first determine the normal elements,
prime ideals and primitive ideals for the algebra $U_{r,s}^{+}(B_{2})$, and
study their stratifications. Then we will prove that the algebra automorphism
group of the algebra $U_{r,s}^{+}(B_{2})$ is isomorphic to
$(\mathbb{C}^{\ast})^{2}$.
