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The division ring of fractions of a group ring

  • Robert L. Snider
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1029)

Keywords

Nilpotent Group Group Algebra Division Algebra Group Ring Division Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S.A. Amitsur and D.J. Saltman, Generic crossed products and p-algebras, J. Algebra 51(1978),76–87.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    S.D. Brodskii, Equations over groups and groups with one defining relation, Uspehi Mat. Nauk 35(1980),183 (Russian).MathSciNetGoogle Scholar
  3. 3.
    G.H. Cliff, Zero divisors and idempotents in group rings, Can. J. Math. 23(1980),596–602.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    D.R. Farkas, Miscellany on Bieberbach group algebras, Pac. J. Math. 59(1975),427–435.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    D.R. Farkas, A.H. Schofield, R.L. Snider, and J.T. Stafford, The isomorphism question for division rings of group rings, Proc. Amer. Math. Soc. (to appear).Google Scholar
  6. 6.
    D.R. Farkas and R.L. Snider, K0 and Noetherian group rings, J. Algebra 42(1976),192–198.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    E. Formanek, Maximal quotient rings of group rings, Pac. J. Math. 53(1974),109–116.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    P. Gabriel and R. Rentschler, Sur la dimension des anneaux et ensembles ordonnes, C.R. Acad. Sci. Paris, Ser. A-B 265(1967) A712–A715.MathSciNetzbMATHGoogle Scholar
  9. 9.
    A. Hattori, Rank element of a projective module, Nagoya J. Math. 25(1965),113–120.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    I.N. Herstein, Noncommutative Rings, Carus Math. Monographs, No. 15, Math. Assoc. Amer. 1968.Google Scholar
  11. 11.
    R. Hirshon, Some cancellation theorems with applications to nilpotent groups, J. Australian Math. Soc. Ser A 23(1977), 147–165.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    J. Howie, On locally indicable groups, Math. Zeit. (to appear).Google Scholar
  13. 13.
    H.W. Lenstra, Rational functions invariant under a finite abelian group, Invent. Math. 25(1974),299–325.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    J. Lewin and T. Lewin, An embedding of the group algebra of a torsion free one-relator group in a field, J. Algebra 52(1978), 39–74.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    A.I. Lichtman, preprint.Google Scholar
  16. 16.
    M. Lorenz, Division algebras generated by finitely generated nilpotent groups, preprint.Google Scholar
  17. 17.
    A.I. Malcev, On embedding of group algebras in a division algebra, Dokl. Akad. Nauk, SSSR 60(1948),1499–1501 (Russian).MathSciNetGoogle Scholar
  18. 18.
    A.S. Merkur’ev and A.A. Suslin, K-cohomologies of Severi-Brauer varieties and norm residue homomorphisms, Dokl. Akad. Nauk. SSSR 264(1982),555–559.MathSciNetzbMATHGoogle Scholar
  19. 19.
    B.H. Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66(1949),202–252.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    D.S. Passman, On the ring of quotients of a group ring, Proc. Amer. Math. Soc. 33(1972),221–225.MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    D.S. Passman, The Algebraic Structure of Group Rings, John Wiley, New York, 1977.zbMATHGoogle Scholar
  22. 22.
    D.S. Passman, Universal fields of fractions of polycyclic group algebras, preprint.Google Scholar
  23. 23.
    R. Resco, Trandscendental division algebras and simple Noetherian rings, Israel J. Math. 32(1979),236–256.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    J.E. Roseblade, Prime ideals in group rings of polycyclic groups, Proc. London Math. Soc. 3(36),1978,385–447.MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    L.H. Rowen and D.J. Saltman, Dihedral algebras are cyclic, Proc. Amer. Math. Soc. 84(1981),162–164.MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    M.K. Smith, Group algebras, J. Algebra 18(1971),477–499.MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    M.K. Smith, Centralizers in rings of quotients of group rings, J. Algebra 25(1973),158–164.MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    R.L. Snider, Is the Brauer group generated by cyclic algebras?, Ring Theory, Lecture notes in Math., Springer, Berlin 1979, No. 734, 279–301.Google Scholar
  29. 29.
    R.L. Snider, The zero divisor conjecture for some solvable groups, Pac. J. Math. 90(1980),191–196.MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    J.T. Stafford, Dimensions of division rings, preprint.Google Scholar
  31. 31.
    J. Stallings, Centerless groups-an algebraic formulation of Gottlieb’s theorem, Topology 4(1965),129–134.MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    A.E. Zalesskii, Irreducible representations of finitely generated nilpotent groups, Math. Notes 9(1971),117–123.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Robert L. Snider
    • 1
  1. 1.Virginia Polytechnic Inst. and State UniversityBlacksburgUSA

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