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Zero-divisors and idempotents in group rings

Malman, Bartosz LU (2014) In Master's Theses in Mathematical Sciences FMA820 20141
Mathematics (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.
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author
Malman, Bartosz LU
supervisor
organization
course
FMA820 20141
year
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},
  keyword      = {algebra,group ring,zero-divisor,idempotent},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {Zero-divisors and idempotents in group rings},
  year         = {2014},
}