We develop theory, and construct examples, of graded rings that have properties similar to the conjectured form of the stable homotopy group of the p-completion of the sphere spectrum π*(Sp) in the p-local stable homotopy category. In particular, these rings are non-Noetherian self injective connected graded rings of finite type that contain at least one non-nilpotent element. Moreover, we also construct examples of non-Noetherian graded rings that have properties similar to the conjectured form of the ring π* (Sp), yet fail to be self injective as graded rings. These examples have an extremely complicated structure, and they also provide counter examples to potential converses to the main theory of self injective graded rings.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:575453 |
| Date | January 2012 |
| Creators | Shepperson, Leigh |
| Publisher | University of Sheffield |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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