This is a preview of subscription content, log in via an institution to check access.
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.A. Amitsur and D.J. Saltman, Generic crossed products and p-algebras, J. Algebra 51(1978),76–87.
S.D. Brodskii, Equations over groups and groups with one defining relation, Uspehi Mat. Nauk 35(1980),183 (Russian).
G.H. Cliff, Zero divisors and idempotents in group rings, Can. J. Math. 23(1980),596–602.
D.R. Farkas, Miscellany on Bieberbach group algebras, Pac. J. Math. 59(1975),427–435.
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).
D.R. Farkas and R.L. Snider, K0 and Noetherian group rings, J. Algebra 42(1976),192–198.
E. Formanek, Maximal quotient rings of group rings, Pac. J. Math. 53(1974),109–116.
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.
A. Hattori, Rank element of a projective module, Nagoya J. Math. 25(1965),113–120.
I.N. Herstein, Noncommutative Rings, Carus Math. Monographs, No. 15, Math. Assoc. Amer. 1968.
R. Hirshon, Some cancellation theorems with applications to nilpotent groups, J. Australian Math. Soc. Ser A 23(1977), 147–165.
J. Howie, On locally indicable groups, Math. Zeit. (to appear).
H.W. Lenstra, Rational functions invariant under a finite abelian group, Invent. Math. 25(1974),299–325.
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.
A.I. Lichtman, preprint.
M. Lorenz, Division algebras generated by finitely generated nilpotent groups, preprint.
A.I. Malcev, On embedding of group algebras in a division algebra, Dokl. Akad. Nauk, SSSR 60(1948),1499–1501 (Russian).
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.
B.H. Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66(1949),202–252.
D.S. Passman, On the ring of quotients of a group ring, Proc. Amer. Math. Soc. 33(1972),221–225.
D.S. Passman, The Algebraic Structure of Group Rings, John Wiley, New York, 1977.
D.S. Passman, Universal fields of fractions of polycyclic group algebras, preprint.
R. Resco, Trandscendental division algebras and simple Noetherian rings, Israel J. Math. 32(1979),236–256.
J.E. Roseblade, Prime ideals in group rings of polycyclic groups, Proc. London Math. Soc. 3(36),1978,385–447.
L.H. Rowen and D.J. Saltman, Dihedral algebras are cyclic, Proc. Amer. Math. Soc. 84(1981),162–164.
M.K. Smith, Group algebras, J. Algebra 18(1971),477–499.
M.K. Smith, Centralizers in rings of quotients of group rings, J. Algebra 25(1973),158–164.
R.L. Snider, Is the Brauer group generated by cyclic algebras?, Ring Theory, Lecture notes in Math., Springer, Berlin 1979, No. 734, 279–301.
R.L. Snider, The zero divisor conjecture for some solvable groups, Pac. J. Math. 90(1980),191–196.
J.T. Stafford, Dimensions of division rings, preprint.
J. Stallings, Centerless groups-an algebraic formulation of Gottlieb’s theorem, Topology 4(1965),129–134.
A.E. Zalesskii, Irreducible representations of finitely generated nilpotent groups, Math. Notes 9(1971),117–123.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Snider, R.L. (1983). The division ring of fractions of a group ring. In: Malliavin, MP. (eds) Séminaire d’Algèbre Paul Dubreil et Marie-Paule Malliavin. Lecture Notes in Mathematics, vol 1029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098938
Download citation
DOI: https://doi.org/10.1007/BFb0098938
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12699-7
Online ISBN: 978-3-540-38686-5
eBook Packages: Springer Book Archive