Geodesic
Idempotents in Noetherian Group Rings
Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 366-369

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If G is a torsion–free group and F is a field, is the group ring F[G] a ring without zero divisors? This is true if G is an ordered group or various generalizations thereof - beyond this the question remains untouched. This paper proves a related result. 
Formanek, Edward. Idempotents in Noetherian Group Rings. Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 366-369. doi: 10.4153/CJM-1973-037-6
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