The browser you are using is not supported by this website. All versions of Internet Explorer are no longer supported, either by us or Microsoft (read more here: https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Please use a modern browser to fully experience our website, such as the newest versions of Edge, Chrome, Firefox or Safari etc.

Zero-divisors and idempotents in group rings

Author

  • Bartosz Malman

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.

Publishing year

2014

Language

English

Publication/Series

Master's Theses in Mathematical Sciences

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