This thesis focuses on the subject of varieties for modules for elementary abelian p-groups. Given a homogeneous polynomial over an algebraically closed field of char- acteristic 2 we will give constructions for modules of small dimension having that polynomial as variety. This is similar to an earlier construction given by Jon Carlson but our modules will in general be of considerably smaller dimension. We also investigate the connection between the variety of a module and its Loewy length. We show that working over an algebraically closed field of characteristic 2 with modules of Loewy length 2 allows us to find modules with any hypersurface as their variety. On the other hand we also demonstrate that in odd characteristic p, with modules of Loewy length p, the only possible varieties are finite unions of linear hypersurfaces.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:600069 |
| Date | January 2013 |
| Creators | Reid, Fergus |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=203509 |
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