Large self-injective rings and the generating hypothesis
Leigh Shepperson, Neil Strickland
TL;DR
This paper constructs examples of non-Noetherian graded rings that are self-injective and explores their connections to triangulated categories and Freyd's Generating Hypothesis in stable homotopy theory.
Contribution
It introduces new examples of non-Noetherian self-injective graded rings and relates them to triangulated categories and the generating hypothesis.
Findings
Examples of non-Noetherian self-injective graded rings are constructed.
Connections between these rings and triangulated categories are discussed.
Implications for Freyd's Generating Hypothesis are analyzed.
Abstract
We construct a number of different examples of non-Noetherian graded rings that are injective as modules over themselves (or have some related but weaker properties). We discuss how these are related to the theory of triangulated categories, and to Freyd's Generating Hypothesis in stable homotopy theory.
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