Chains of group localizations

TL;DR

This paper constructs long sequences of localization functors in the category of abelian groups, demonstrating proper inclusions for large free abelian groups and a range of infinite cardinals.

Contribution

It introduces a method to create chains of localization functors with proper inclusions at infinite cardinals, expanding understanding of localizations in abelian groups.

Findings

Proper inclusions of localizations for large free abelian groups

Construction of long chains of localization functors

Demonstration of localizations at infinite cardinals

Abstract

We construct long sequences of localization functors L_a in the category of abelian groups such that L_a > L_b for infinite cardinals a < b less than some k. For sufficiently large free abelian groups F and a < b we have proper inclusions of L_aF into L_bF.