Zero-divisors and idempotents in group rings
(2014) In Master's Theses in Mathematical Sciences FMA820 20141Mathematics (Faculty of Engineering)
- Abstract
- 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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/4611218
- author
- Malman, Bartosz LU
- supervisor
- organization
- course
- FMA820 20141
- year
- 2014
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- algebra, group ring, zero-divisor, idempotent
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUTFMA-3265-2014
- ISSN
- 1404-6342
- other publication id
- 2014:E45
- language
- English
- id
- 4611218
- date added to LUP
- 2014-10-07 12:27:09
- date last changed
- 2014-10-07 12:27:09
@misc{4611218, abstract = {{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.}}, author = {{Malman, Bartosz}}, issn = {{1404-6342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master's Theses in Mathematical Sciences}}, title = {{Zero-divisors and idempotents in group rings}}, year = {{2014}}, }