Units in Non-Commutative Orders

Research output: ThesisPhD Thesis

Abstract

For a ring R with unity 1, we denote by U(R) the unit group of R, i.e. the group of invertible elements in R. For decades one has investigated the unit group of an integral group ring Z[G] of a group G. These rings are very interesting algebraic structures, because of their obvious relationship with group theory and ring theory and because the investigations in the structure also involve for example the theory of fields, linear algebra, alge- braic topology, algebraic number theory and algebraic K-theory. Hence the research in group rings is a subject where many branches of algebra meet. In the study of group rings the knowledge of the unit group is crucial, but a complete description of the unit group in terms of generators and relations still seems out of reach, even for special classes of groups.
Original languageEnglish
QualificationDoctor of Sciences
Awarding Institution
  • Vrije Universiteit Brussel
Supervisors/Advisors
  • Jespers, Eric, Supervisor
Award date26 Mar 2004
Place of PublicationBrussels
Publication statusPublished - Mar 2004

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