This is again an abelian group. Usually "E" is an "additive" abelian group. If "E" has additional algebraic structure compatible with the filtration, for instance "E" is a filtered ring, a filtered module, or a filtered vector space, then its completion is again an object with the same structure that is complete in the topology determined by the filtration. This construction may be applied both to commutative and noncommutative rings. As may be expected, when the intersection of the formula_3 equals zero, this produces a complete topological ring.