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