CompletedGroupAlgebra.ProfiniteModules.Basic

5 sections | 5 files | 70 declarations

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.

Definitions

1 files | 27 declarations | 16 Theorem | 10 Definition | 1 Structure

A compact Hausdorff totally disconnected topological ring.

FiniteQuotients

1 files | 10 declarations | 9 Theorem | 1 Abbreviation

In Lemma 5.1.1(b), linear-topology interface, a profinite module with a linear topology has a basis of open finite-index submodules at zero.

Generators

1 files | 12 declarations | 8 Theorem | 4 Definition

A subset converges to zero in the all-but-finitely-many-elements sense used in the book.

OpenIdeals

1 files | 12 declarations | 9 Theorem | 3 Definition

Open ideals form a neighborhood basis at zero.

OpenSubmodule

1 files | 9 declarations | 8 Theorem | 1 Definition

A compact Hausdorff totally disconnected additive group has arbitrarily small open additive subgroups at zero.