CompletedGroupAlgebra

The canonical augmentation ideal \(I_G\subseteq \widehat{R[G]}\) is the kernel of the completed augmentation \(\varepsilon:\widehat{R[G]}\to R\).

The inverse image of an open-finite quotient of \(H\) along a continuous homomorphism \(G\to H\), regarded as an open-finite quotient of the profinite group \(G\). This is the i...

The canonical augmentation ideal of the \(C\)-indexed completed group algebra.

The carrier of the completed group algebra is the inverse limit \(\widehat{R[G]}=\varprojlim_U R[G/U]\) over the open-normal finite quotients of \(G\).

This module proves that completed group algebra functoriality is compatible with composition.

Completed Group Algebra / Functoriality Within a Class / Comap Index.

The quotient map from the abstract group algebra \(R[G]\) to one \(C\)-indexed finite stage.

A compact Hausdorff totally disconnected topological ring.

This module proves separation lemmas for completed group algebras using finite quotients.

The concrete inverse-limit construction satisfies the universal-property specification for the completed group algebra.