165
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Free Fields in Malcev–Neumann Series Rings

, &
Pages 1149-1168 | Received 16 Aug 2011, Published online: 13 Mar 2013

REFERENCES

  • Bavula , V. V. ( 2008 ). Finite generation of the group of eigenvalues for sets of derivations or automorphisms of division algebras . Comm. Algebra 36 : 2195 – 2201 .
  • Botto Mura , R. , Rhemtulla , A. ( 1977 ). Orderable Groups . New York–Basel : Marcel Dekker .
  • Chiba , K. ( 2003 ). Free fields in complete skew fields and their valuations . J. Algebra 263 : 75 – 87 .
  • Cohn , P. M. ( 1977 ). Skew Field Constructions . Cambridge–New York–Melbourne : Cambridge University Press .
  • Cohn , P. M. ( 1985 ). Free Rings and Their Relations . Second Edition. London : Academic Press .
  • Cohn , P. M. ( 1995 ). Skew Fields. Theory of General Division Rings . Cambridge : Cambridge University Press .
  • Dicks , W. , Lewin , J. ( 1982 ). A Jacobian conjecture for free associative algebras . Comm. Algebra 10 : 1285 – 1306 .
  • Elek , G. ( 2006 ). The amenability and non-amenability of skew fields . Proc. Amer. Math. Soc. 134 : 637 – 644 .
  • Fuchs , L. ( 1963 ). Partially Ordered Algebraic Systems . Oxford–London–New York–Paris : Pergamon Press .
  • Gonçalves , J. Z. , Shirvani , M. ( 2012 ). A survey on free objects in division rings and in division rings with an involution . Comm. Algebra 40 : 1704 – 1723 .
  • Hughes , I. ( 1970 ). Division rings of fractions for group rings . Comm. Pure Appl. Math. 23 : 181 – 188 .
  • Jennings , S. A. ( 1955 ). The group ring of a class of infinite nilpotent groups . Canad. J. Math. 7 : 169 – 187 .
  • Lam , T. Y. ( 1999 ). Lectures on Modules and Rings . New York : Springer-Verlag .
  • Lam , T. Y. ( 2001 ). A First Course in Noncommutative Rings . Second Edition. New York : Springer-Verlag .
  • Lewin , J. ( 1974 ). Fields of fractions for group algebras of free groups . Trans. Amer. Math. Soc. 192 : 339 – 346 .
  • Lichtman , A. I. ( 1977 ). On subgroups of the multiplicative group of skew fields . Proc. Amer. Math. Soc. 63 : 15 – 16 .
  • Lichtman , A. I. ( 1995 ). Valuation methods in division rings . J. Algebra 177 : 870 – 898 .
  • Lichtman , A. I. ( 1999 ). Free subalgebras in division rings generated by universal enveloping algebras . Algebra Colloq. 6 : 145 – 153 .
  • Makar-Limanov , L. ( 1983 ). The skew field of fractions of the Weyl algebra contains a free noncommutative subalgebra . Comm. Algebra 11 : 2003 – 2006 .
  • Makar-Limanov , L. ( 1984 ). On group rings of nilpotent groups . Israel J. Math. 48 : 244 – 248 .
  • Makar-Limanov , L. , Malcolmson , P. (1991). Free subalgebras of enveloping fields. Proc. Amer. Math. Soc. 111:315–322.
  • Mal'cev , A. I. ( 1948 ). On the embedding of group algebras in division algebras . Doklady Akad. Nauk SSSR (N. S.) 60 : 1499 – 1501 .
  • Navas , A. , Rivas , C. ( 2010 ). Describing all bi-orderings on Thompson's group . F. Groups Geom. Dyn. 4 : 163 – 177 .
  • Neumann , B. H. ( 1949 ). On ordered division rings . Trans. Amer. Math. Soc. 66 : 202 – 252 .
  • Passman , D. S. ( 1989 ). Infinite Crossed Products . Boston , MA : Academic Press .
  • Sweedler , M. E. ( 1980 ). Tensor products of division rings and finite generation of subdivision rings . Bull. Inst. Math. Acad. Sinica 8 : 385 – 387 .
  • Communicated by I. Shestakov.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.