Zero-divisors and idempotents in group rings
Author
Summary, in English
After a brief introduction of the basic properties of group rings, some famous theorems on traces of idempotent elements of group rings will be presented. Next we consider some famous conjectures stated by Irving Kaplansky, among them the zero-divisor conjecture. The conjecture asserts that if a group ring is constructed from a field (or an integral domain) and a torsion-free group, then it does not contain any non-trivial zero-divisors. Here we show how a confirmation of the conjecture for certain fields implies its validity for other fields.
Department/s
Publishing year
2014
Language
English
Publication/Series
Master's Theses in Mathematical Sciences
Full text
- Available as PDF - 403 kB
- Download statistics
Document type
Student publication for Master's degree (two years)
Topic
- Mathematics and Statistics
Keywords
- algebra
- group ring
- zero-divisor
- idempotent
Report number
LUTFMA-3265-2014
Supervisor
- Johan Öinert (Docent)
Scientific presentation
ISBN/ISSN/Other
- ISSN: 1404-6342
- 2014:E45