Erfüllbarkeit und Gruppenringe

• Antragsteller: Professor Dr. Giles Gardam
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2022 bis 2024
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 506523109

• Erstellungsjahr: 2024

Zusammenfassung der Projektergebnisse

The unit conjecture for group rings predicts that the group ring of a torsion-free group over a field has only trivial units, i.e. scalar multiples of group elements. It was known that the conjecture is false for positive characteristic fields. In this project we showed that it is also false in the remaining and arguably most important case, namely in characteristic zero. Finding integral units and counterexamples to other conjectures of Kaplansky will be the subject of future work.

Projektbezogene Publikationen (Auswahl)

• Graphs and groups with unique geodesics
  Murray Elder; Giles Gardam; Adam Piggott; Davide Spriano & Kane Townsend
  
• Non-trivial units of complex group rings
  Giles Gardam