Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T01:35:07.860Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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