CompletedGroupAlgebra.OpenFiniteQuotientTopology.OpenFiniteLimit
The completed group algebra is presented as an inverse limit of finite group algebras, together with canonical augmentation, augmentation ideal, finite-stage maps, functoriality, and profinite module universal properties.
Algebra
The zero element is defined coordinatewise as the compatible family of zero elements at all finite stages.
CanonicalMap
The abstract group-algebra map onto an open-finite quotient stage is surjective.
System
The two-parameter inverse system \(K = (I, U) \mapsto (R/I)[G/U]\) for the kernel-neighborhood topology.
Topology
Each two-parameter finite quotient stage is a topological ring for its discrete topology.