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We develop a method of representation of distributive (V,0,1)-semilattices as semilattices of finitely generated ideals of locally matricial algebras. We use the method to reprove two representation results by G. M. Bergman and prove a new one that every distributive (0,1)-lattice is, as a semilattice, isomorphic to the semilattice of all finitely generated ideals of a locally matricial algebra. We apply this fact to solve the Γ-invariant problem.