Discrete module categories and operations in K-theory

TL;DR

This paper investigates the structure of discrete modules over topological rings associated with topological K-theory, establishing a key equivalence with locally finitely generated modules.

Contribution

It proves that for these rings, discrete modules are exactly those modules that are locally finitely generated over the ground ring.

Findings

Discrete modules coincide with locally finitely generated modules.

The study clarifies the module structure in topological K-theory contexts.

Provides foundational results for module categories in algebraic topology.

Abstract

We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally finitely generated over the ground ring.