Stable finiteness of group rings in arbitrary characteristic

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

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

Stable finiteness of group rings in arbitrary characteristic

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

Departament de Matemàtiques

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Resum

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).

Idioma original	Anglès
Pàgines (de-a)	224-238
Revista	Advances in Mathematics
Volum	170
DOIs	https://doi.org/10.1016/S0001-8708(02)92075-X
Estat de la publicació	Publicada - 25 de set. 2002

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10.1016/S0001-8708(02)92075-X

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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).",

author = "Francesc Perera and O'Meara, {Kevin C.} and Pere Ara",

year = "2002",

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doi = "10.1016/S0001-8708(02)92075-X",

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T1 - Stable finiteness of group rings in arbitrary characteristic

AU - Perera, Francesc

AU - O'Meara, Kevin C.

AU - Ara, Pere

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).

UR - https://dialnet.unirioja.es/servlet/articulo?codigo=315392

U2 - 10.1016/S0001-8708(02)92075-X

DO - 10.1016/S0001-8708(02)92075-X

M3 - Article

SN - 0001-8708

VL - 170

SP - 224

EP - 238

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Stable finiteness of group rings in arbitrary characteristic

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