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 $\Gamma(X) = \Gamma(Y)$.
Categories: math.AC math.RA