Abstract
Let G be a group and let K be a field of characteristic zero. We shall prove that KG can be embedded into a von Neumann unit-regular ring. In the course of the proof, we shall obtain a result relevant to the Atiyah conjecture.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S.K. Berberian. The maximal ring of quotients of a finite von Neumann algebra. Rocky Mountain J. Math., 12(1):149–164, 1982.
Sterling K. Berberian. Baer *-rings. Springer-Verlag, New York, 1972. Die Grundlehren der mathematischen Wissenschaften, Band 195.
K. Bonvallet, B. Hartley, D.S. Passman, and M.K. Smith. Group rings with simple augmentation ideals. Proc. Amer. Math. Soc., 56:79–82, 1976.
Gábor Elek and Endre Szabó. Sofic groups and direct finiteness. J. Algebra, 280(2):426–434, 2004.
Carl Faith. Dedekind finite rings and a theorem of Kaplansky. Comm. Algebra, 31(9):4175–4178, 2003.
K.R. Goodearl. von Neumann regular rings. Robert E. Krieger Publishing Co. Inc., Malabar, FL, second edition, 1991.
Richard V. Kadison and John R. Ringrose. Fundamentals of the theory of operator algebras. Vol. II, volume 16 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1997. Advanced theory, Corrected reprint of the 1986 original.
Dinesh Khurana and T.Y. Lam. Rings with internal cancellation. J. Algebra, 284(1):203–235, 2005.
Wolfgang LĂĽck. L 2-invariants: theory and applications to geometry and K-theory, volume 44 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Springer-Verlag, Berlin, 2002.
W.R. Scott. Algebraically closed groups. Proc. Amer. Math. Soc., 2:118–121, 1951.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Linnell, P.A. (2008). Embedding Group Algebras into Finite von Neumann Regular Rings. In: Brzeziński, T., Gómez Pardo, J.L., Shestakov, I., Smith, P.F. (eds) Modules and Comodules. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8742-6_19
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8742-6_19
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8741-9
Online ISBN: 978-3-7643-8742-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)