  In this paper we investigate extended modules for a special class of Ore
extensions. We will assume that $R$ is a ring and $A$ will denote the Ore
extension $A:=R[x_1,\dots,x_n;\sigma]$ for which $\sigma$ is an automorphism of
$R$, $x_ix_j=x_jx_i$ and $x_ir=\sigma(r)x_i$, for every $1\leq i,j\leq n$. With
some extra conditions over the ring $R$, we will prove Vaserstein's, Quillen's
patching, Horrocks' and Quillen-Suslin's theorems for this type of
non-commutative rings.
