The Cyclical Compactness in Banach C∞(Q)-Modules

In this paper we study the class of laterally complete commutative unital regular algebras A over arbitrary fields. We introduce a notion passport Γ(X) for faithful Amodules X, which consist uniquely defined partition unity in Boolean algebra all idempotents and set pairwise different cardinal numbers. prove that A-modules X Y are isomorphic if only = Γ(Y). Further Banach case C∞(Q) or C∞(Q)+i ·C∞(Q). establish equivalence norms finite-dimensional (respectively, σ-finite-dimensional) A-module an A-version Riesz Theorem, gives criterion finite-dimensionality σ-finite-dimensionality) A-module.