Kaplansky’s conjectures and actions on CAT(-1) Spaces
| dc.contributor.advisor | Touikan, Nicholas | |
| dc.contributor.author | Brannock, Matthew | |
| dc.date.accessioned | 2024-03-06T15:04:34Z | |
| dc.date.available | 2024-03-06T15:04:34Z | |
| dc.date.issued | 2023-11 | |
| dc.description.abstract | We provide specific conditions on a ring R and a group G under which the group ring RG will satisfy the Kaplansky Conjectures on the existence of non-trivial units, zero-divisors and idempotents in the group ring. We give a chain of implications on properties that a group must have to satisfy these conjectures. Specifically, we define a Bowditch action of a group on a type of metric space called a CAT(-1) space and show this action will be spherically diffuse. We then prove that if a group acts on a metric space in a spherically diffusely, then the group itself must be diffuse. Next we prove that if a group is diffuse then it satisfies the Unique Product Property. We then prove that if a group satisfies this property, then the group ring formed by this group and any integral domain will satisfy the Kaplansky Conjectures. | |
| dc.description.copyright | © Matthew Brannock, 2023 | |
| dc.format.extent | vii, 82 | |
| dc.format.medium | electronic | |
| dc.identifier.oclc | (OCoLC)1439830961 | en |
| dc.identifier.other | Thesis 11335 | en |
| dc.identifier.uri | https://unbscholar.lib.unb.ca/handle/1882/37744 | |
| dc.language.iso | en | |
| dc.publisher | University of New Brunswick | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.subject.discipline | Mathematics and Statistics | |
| dc.subject.lcsh | Prediction (Logic) | en |
| dc.subject.lcsh | Group theory. | en |
| dc.subject.lcsh | Class groups (Mathematics) | en |
| dc.title | Kaplansky’s conjectures and actions on CAT(-1) Spaces | |
| dc.type | master thesis | |
| oaire.license.condition | other | |
| thesis.degree.discipline | Mathematics and Statistics | |
| thesis.degree.grantor | University of New Brunswick | |
| thesis.degree.level | masters | |
| thesis.degree.name | M.Sc. |