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Algebraic elements in matrix ring over division algebras*

Published online by Cambridge University Press:  24 October 2008

A. I. Lichtman
A. I. Lichtman
Affiliation:
Department of Mathematics, University of Wisconsin-Parkside, Kenosha, WI 53141, U.S.A.
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Extract

Let K be an arbitrary field, G a polycyclic-by-finite group and A a prime ideal of the group ring KG. It is well known that the quotient ring (KG)/A is a Goldie ring; we denote by R its ring of fractions. Let U be a subgroup of units of the matrix ring Rn×n let K[U] be the linear envelope of U and let rad (K[U]) be the nilpotent radical of K [U].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 215 - 221
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1]Lichtman, A. I.. On linear groups over the fields of fractions of a polycyclic group ring. Israel J. Math. 42 (1982), 318–326.Google Scholar
[2]Rowen, L. H.. Polynomial identities in ring theory (Academic Press, 1980).Google Scholar
[3]Lichtman, A. I. and Wehrfritz, B. A. F.. Finite dimensional subalgebras in matrix rings over transcendental division algebras. Proc. Amer. Math. Soc. 106 (1989), 335–344.Google Scholar
[4]Passman, D. S.. The algebraic structure of group rings, Wiley and Sons, New York, 1977.Google Scholar
[5]Roseblade, J. E.. Prime ideals in group rings of polycyclic groups. Proc. London Math. Soc. (3) 36 (1978), 385–447.Google Scholar
[6]Shirvani, M. and Wehrfritz, B. A. F.. Skew linear groups (Cambridge University Press, 1986).Google Scholar
[7]Jacobson, N.. Structure of rings. (Amer. Math. Soc., 1956).Google Scholar
[8]Lichtman, A. I.. On nilpotent and soluble subgroups of linear groups over fields of fractions of enveloping algebras and of group rings, I. Contemporary Mathematics 93 (1989), 247–281.Google Scholar
[9]Jacobson, N.. Lie algebras (Wiley, 1962).Google Scholar