dc.contributor.author | Connon, Emma | |
dc.date.accessioned | 2013-11-07T13:40:23Z | |
dc.date.available | 2013-11-07T13:40:23Z | |
dc.date.issued | 2013-11-07 | |
dc.identifier.uri | http://hdl.handle.net/10222/38565 | |
dc.description.abstract | In 1990, Fröberg presented a combinatorial classification of the quadratic square-free monomial ideals with linear resolutions. He showed that the edge ideal of a graph has a linear resolution if and only if the complement of the graph is chordal. Since then, a generalization of Fröberg's theorem to higher dimensions has been sought in order to classify all square-free monomial ideals with linear resolutions. Such a characterization would also give a description of all square-free monomial ideals which are Cohen-Macaulay.
In this thesis we explore one method of extending Fröberg's result. We generalize the idea of a chordal graph to simplicial complexes and use simplicial homology as a bridge between this combinatorial notion and the algebraic concept of a linear resolution. We are able to give a generalization of one direction of Fröberg's theorem and, in investigating the converse direction, find a necessary and sufficient combinatorial condition for a square-free monomial ideal to have a linear resolution over fields of characteristic 2. | en_US |
dc.language.iso | en | en_US |
dc.subject | monomial ideals | en_US |
dc.subject | linear resolution | en_US |
dc.subject | Fröberg's Theorem | en_US |
dc.subject | chordal graph | en_US |
dc.subject | Stanley-Reisner ideal | en_US |
dc.subject | simplicial complex | en_US |
dc.subject | simplicial homology | en_US |
dc.title | Generalizing Fröberg's Theorem on Ideals with Linear Resolutions | en_US |
dc.date.defence | 2013-10-07 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Doctor of Philosophy | en_US |
dc.contributor.external-examiner | Winfried Bruns | en_US |
dc.contributor.graduate-coordinator | Sara Faridi | en_US |
dc.contributor.thesis-reader | Dorette Pronk | en_US |
dc.contributor.thesis-reader | Jason Brown | en_US |
dc.contributor.thesis-supervisor | Sara Faridi | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Yes | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |