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Trace Functions in the Ring of Fractions of Polycyclic Group Rings, II

Published online by Cambridge University Press:  20 November 2018

A. I. Lichtman
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Abstract

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We prove the existence of trace functions in the rings of fractions of polycyclic-by-finite group rings or their homomorphic images. In particular a trace function exists in the ring of fractions of KH, where H is a polycyclic-by-finite group and char K > N, where N is a constant depending on H.

Keywords

20C0716A0816A39
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 788 - 797
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Amitsur, S. and Rowen, L., Elements of reduced trace zero. Israel J. Math. 87(1994), 1–3. 161–179.Google Scholar
2. Hartley, B.H., Topics in the theory of nilpotent groups, Group Theory, Essays for Philip Hall, Academic Press, New York, 1984. 61–120.Google Scholar
3. Hattori, A., Rank element of a projective module. Nagoya J. Math. 15(1965), 113–120.Google Scholar
4. Lichtman, A.I., The residual nilpotence of the augmentation ideal and the residual nilpotence of some classes of groups. Israel J. Math. 26(1977), 276–293.Google Scholar
5. Lichtman, A.I., On PI-subrings of matrix rings over some classes of a skew fields. J. Pure and Appl. Algebra 52(1988), 77–89.Google Scholar
6. Lichtman, A.I., Trace functions in the ring of fractions of polycyclic group rings. Trans. Amer.Math. Soc. 330(1992), 769–781.Google Scholar
7. Lichtman, A.I., The soluble subgroups and the Tits alternative in linear groups over rings of fractions of polycyclic group rings, I. J. Pure Appl. Algebra 86(1993), 231–287.Google Scholar
8. Lichtman, A.I., Algebraic elements in matrix rings over division algebras. Math. Proc. Cambridge Phil. Soc. 118(1995), 215–221.Google Scholar
9. Lorenz, M., Group rings and division rings, Proc. Nat. ASI,Methods in Ring Theory, Reidel, Boston, MA, (1984), 265–280.Google Scholar
10. Lorenz, M., Crossed products, cyclic homology, and Grothendieck groups. Noncommutative Rings 24, MSRI Publications, Springer, New York, 1992.Google Scholar
11. Passman, D.S., The Algebraic Structure of Group Rings, Wiley-Interscience, New York, 1977.Google Scholar
12. Lorenz, M., Universal fields of fractions for polycyclic group algebras. Glasgow Math. J. 23(1982), 103–113.Google Scholar
13. Roseblade, J., Group rings of polycyclic groups. J. Pure Appl. Algebra 31(1973), 307–328.Google Scholar
14. Shirvany, M. and Wehrfritz, B.A.F., Linear Groups. London Math. Society Lecture Notes 118, Cambridge Univ. Press, Cambridge, 1986.Google Scholar
15. Snider, R.L., The division ring of fractions of a group ring. Lecture Notes in Math. 1029, Springer-Verlag, 1983. 325–339.Google Scholar
16. Stallings, J., Centerless group—an algebraic formulation of Gottlieb's theorem. Topology 4(1965), 129– 134.Google Scholar