Geodesic
On stable finiteness of group rings
Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 44-47.

Voir la notice de l'article provenant de la source Math-Net.Ru

For an arbitrary field or division ring $K$ and an arbitrary group $G$, stable finiteness of $K[G]$ is equivalent to direct finiteness of $K[G\times H]$ for all finite groups $H$.
Keywords: Kaplansky's Direct Finiteness Conjecture, stable finiteness. 
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K. Dykema; K. Juschenko. On stable finiteness of group rings. Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 44-47. http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a5/

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[2] K. Dykema, T. Heister, and K. Juschenko, “Finitely presented groups related to Kaplansky's Direct Finiteness Conjecture”, Exp. Math. (to appear) | MR

[3] G. Elek and E. Szabó, “Sofic groups and direct finiteness”, J. Algebra, 280 (2004), 426–434 | DOI | MR | Zbl

[4] I. Kaplansky, Fields and rings, The University of Chicago Press, 1969 | MR