  We define the completion of an associative algebra $A$ in a set
$M=\{M_1,\dots,M_r\}$ of $r$ right $A$-modules in such a way that if $\mathfrak
a\subseteq A$ is an ideal in a commutative ring $A$ the completion $A$ in the
(right) module $A/\mathfrak a$ is $\hat A^M\simeq \hat A^{\mathfrak a}.$ This
works by defining $\hat A^M$ as a formal algebra determined up to a computation
in a category called GMMP-algebras. From deformation theory we get that the
computation results in a formal algebra which is the prorepresenting hull of
the noncommutative deformation functor, and this hull is unique up to
isomorphism.
