Laterally complete regular modules

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

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