Geodesic
Trace Functions in the Ring of Fractions of Polycyclic Group Rings, II
Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 788-797

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1997-039-1
Mots-clés : 20C07, 16A08, 16A39 
Trace Functions in the Ring of Fractions of Polycyclic Group Rings, II. Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 788-797. doi: 10.4153/CJM-1997-039-1
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[1] 1. Amitsur, S. and Rowen, L., Elements of reduced trace zero. Israel J. Math. 87(1994), 1–3. 161–179. Google Scholar

[2] 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] 3. Hattori, A., Rank element of a projective module. Nagoya J. Math. 15(1965), 113–120. Google Scholar

[4] 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] 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] 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] 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] 8. Lichtman, A.I., Algebraic elements in matrix rings over division algebras. Math. Proc. Cambridge Phil. Soc. 118(1995), 215–221. Google Scholar

[9] 9. Lorenz, M., Group rings and division rings, Proc. Nat. ASI,Methods in Ring Theory, Reidel, Boston, MA, (1984), 265–280. Google Scholar

[10] 10. Lorenz, M., Crossed products, cyclic homology, and Grothendieck groups. Noncommutative Rings 24, MSRI Publications, Springer, New York, 1992. Google Scholar

[11] 11. Passman, D.S., The Algebraic Structure of Group Rings, Wiley-Interscience, New York, 1977. Google Scholar

[12] 12. Lorenz, M., Universal fields of fractions for polycyclic group algebras. Glasgow Math. J. 23(1982), 103–113. Google Scholar

[13] 13. Roseblade, J., Group rings of polycyclic groups. J. Pure Appl. Algebra 31(1973), 307–328. Google Scholar

[14] 14. Shirvany, M. and Wehrfritz, B.A.F., Linear Groups. London Math. Society Lecture Notes 118, Cambridge Univ. Press, Cambridge, 1986. Google Scholar

[15] 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] 16. Stallings, J., Centerless group—an algebraic formulation of Gottlieb's theorem. Topology 4(1965), 129– 134. Google Scholar

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