Stable finiteness of group rings in arbitrary characteristic

Pere Ara; Kevin C. O'Meara; Francesc Perera

doi:https://doi.org/10.1016/S0001-8708(02)92075-X

Stable finiteness of group rings in arbitrary characteristic

Pere Ara, Kevin C. O'Meara, Francesc Perera

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

16 Citations (Scopus)

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. © 2002 Elsevier Science (USA).

Original language	English
Pages (from-to)	224-238
Journal	Advances in Mathematics
Volume	170
DOIs	https://doi.org/10.1016/S0001-8708(02)92075-X
Publication status	Published - 25 Sep 2002

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title = "Stable finiteness of group rings in arbitrary characteristic",

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. {\textcopyright} 2002 Elsevier Science (USA).",

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AU - Ara, Pere

AU - O'Meara, Kevin C.

AU - Perera, Francesc

PY - 2002/9/25

Y1 - 2002/9/25

N2 - 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. © 2002 Elsevier Science (USA).

AB - 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. © 2002 Elsevier Science (USA).

U2 - https://doi.org/10.1016/S0001-8708(02)92075-X

DO - https://doi.org/10.1016/S0001-8708(02)92075-X

M3 - Article

VL - 170

SP - 224

EP - 238

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

Stable finiteness of group rings in arbitrary characteristic

Abstract

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