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Stable Finiteness of Group Rings in Arbitrary Characteristic |
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| Authors: | Pere Ara Kevin C. O'Meara Francesc Perera |
| Affiliation: | a Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spainf1;b Department of Mathematics, University of Canterbury, Christchurch, New Zealandf2;c Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spainf3f4 |
| Abstract: | We show that every (discrete) group ring D[G] of a free-by-amenable group G over a division ring D of arbitrary characteristic is stably finite, in the sense that one-sided inverses in all matrix rings over D[G] are two-sided. Our methods use Sylvester rank functions and the translation ring of an amenable group. |
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