# Characterizing Zero Divisors of Group Rings

 dc.contributor.author Welch, Amanda Renee en dc.contributor.committeechair Linnell, Peter A. en dc.contributor.committeemember Rossi, John F. en dc.contributor.committeemember Floyd, William J. en dc.contributor.committeemember Brown, Ezra A. en dc.contributor.department Mathematics en dc.date.accessioned 2015-06-17T08:01:20Z en dc.date.available 2015-06-17T08:01:20Z en dc.date.issued 2015-06-15 en dc.description.abstract The 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 ๐บ. There are examples showing that the conjecture does not hold in general. These examples involve something like the lamplighter group (the wreath product โค/2โค โ โค). We are interested in looking at examples where this is not the case. We are interested in the specific case where ๐บ is a finitely generated group in which the Prรผfer group can be embedded as the center. The Prรผfer group is a ๐-group for some prime ๐ 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 ๐บ, it will first help to determine whether the group ring ๐๐บ of the group ๐บ has a classical ring of quotients for some field ๐. To determine this we will need to know the zero divisors for the group ring ๐๐บ. Our investigations will be divided into two cases, namely when the characteristic of the field ๐ is the same as the prime p for the Prรผfer group and when it is different. en dc.description.degree Master of Science en dc.format.medium ETD en dc.identifier.other vt_gsexam:5513 en dc.identifier.uri http://hdl.handle.net/10919/52949 en dc.publisher Virginia Tech en dc.rights In Copyright en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject Prufer Group en dc.subject zero divisors en dc.subject group rings en dc.subject p-groups en dc.title Characterizing Zero Divisors of Group Rings en dc.type Thesis en thesis.degree.discipline Mathematics en thesis.degree.grantor Virginia Polytechnic Institute and State University en thesis.degree.level masters en thesis.degree.name Master of Science en

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