Classification of modules over laterally complete regular algebras

الأصل · EN

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 Γ(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 Γ(X) = Γ(Y).