Show simple item record

dc.contributor.authorWelch, Amanda Reneeen_US
dc.date.accessioned2015-06-17T08:01:20Z
dc.date.available2015-06-17T08:01:20Z
dc.date.issued2015-06-15en_US
dc.identifier.othervt_gsexam:5513en_US
dc.identifier.urihttp://hdl.handle.net/10919/52949
dc.description.abstractThe Atiyah Conjecture originates from a paper written 40 years ago by Sir Michael Atiyah, a famous mathematician and Fields medalist. Since publication of the paper, mathematicians have been working to solve many questions related to the conjecture, but it is still open. The conjecture is about certain topological invariants attached to a group G. There are examples showing that the conjecture does not hold in general. These examples involve something like the lamplighter group. We are interested in looking at examples where this is not the case. We are interested in the specific case where G is a finitely generated group in which the Pr'ufer group can be embedded as the center. The Pr'ufer group is a p-group for some prime p and its finite subgroups have unbounded order, in particular the finite subgroups of G will have unbounded order. To understand whether any form of the Atiyah conjecture is true for G, it will first help to determine whether the group ring kG of the group G has a classical ring of quotients for some field k. To determine this we will need to know the zero divisors for the group ring kG. Our investigations will be divided into two cases, namely when the characteristic of the field k is the same as the prime p for the Pr'ufer group and when it is different.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectPrufer Groupen_US
dc.subjectzero divisorsen_US
dc.subjectgroup ringsen_US
dc.subjectp-groupsen_US
dc.titleCharacterizing Zero Divisors of Group Ringsen_US
dc.typeThesisen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreeMaster of Scienceen_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairLinnell, Peter A.en_US
dc.contributor.committeememberRossi, John F.en_US
dc.contributor.committeememberFloyd, William J.en_US
dc.contributor.committeememberBrown, Ezra A.en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record