Geodesic
One-Sided Inverses in Rings
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 218-224

Voir la notice de l'article provenant de la source Cambridge University Press

Following Herstein [2], we will call a ring R with identity von Neumann finite (vNf) provided that xy = 1 implies yx — WnR. Kaplansky [4] showed that group algebras over fields of characteristic zero are vNf rings, and further, that full matrix rings over such rings are also vNf. Herstein [2] has posed the problem for group algebras over fields of arbitrary characteristic. If group algebras over fields are always vNf, then it is easily seen that group algebras over commutative rings are always vNf. What conditions on the underlying ring of scalars would force the vNf property for all group rings over it? 
Peterson, Roger D. One-Sided Inverses in Rings. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 218-224. doi: 10.4153/CJM-1975-026-3
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