Reflexive Modules, the Infinite Root Algebra and the Generating Hypothesis
Algebraic Topology
2025-08-12 v1 K-Theory and Homology
Abstract
This thesis concerns the algebraic consequences of Freyd's Generating Hypothesis, and explores the question of whether there exists a self-injective ring R that can be constructed purely algebraically that exhibits some of the known properties of the stable homotopy ring, including some conjectured properties that follow from Freyd's Generating Hypothesis. As an example, we investigate the infinite root algebra of Hahn series P, firstly by establishing results for the related Hahn ring A. In particular, we prove that the Theta-reflexive A-modules and the multibasic A-modules are the same.
Cite
@article{arxiv.2508.07116,
title = {Reflexive Modules, the Infinite Root Algebra and the Generating Hypothesis},
author = {Oliver House},
journal= {arXiv preprint arXiv:2508.07116},
year = {2025}
}
Comments
159 pages, PhD thesis, University of Sheffield, 2025