Conditions so that a finite number of elementsf0fnof a functionF-algebra A can generate A as an A-module are considered from various points of view. In several cases, simple explicit algebraic tools are presented to reduce the problem of finding the coefficients of a representation of 1 to integrations in suitable algebraic complexes (sometimes, it is a question of integration of ∂exact forms). Applications to algebras of holomorphic functions on domains X with strictly pseudoconvex boundary are described. especially when the considered functions have rather regular behavior up to the boundary of X.