  Let $\mathcal{A}$ be a laterally complete commutative regular algebra and $X$
be a laterally complete $\mathcal{A}$-module. In this paper we introduce a
notion of passport $\Gamma(X)$ for $X$, which consist of uniquely defined
partition of unity in the Boolean algebra of idempotents in $\mathcal{A}$ and
the set of pairwise different cardinal numbers. It is proved that
$\mathcal{A}$-modules $X$ and $Y$ are isomorphic if and only if $\Gamma(X) =
\Gamma(Y)$.
