Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-31T08:37:31.033Z Has data issue: false hasContentIssue false
  • English
  • Français

Some homomorphisms of general and special linear groups

Published online by Cambridge University Press:  14 November 2011

A. W. Mason
A. W. Mason
Affiliation:
Department of Mathematics, The University, Glasgow G12 8QW, U.K.
Get access Rights & Permissions [Opens in a new window]

Synopsis

A ring epimorphism θ:A →B extends in a natural way to a homomorphism γn: GLn(A)→GLn(B) and, when A is commutative, to a homomorphism σn:SLn(A)→SLn(B), where n ≧ 1. In this paper we consider the question: when are γn and σn surjective (or non-surjective)?

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 287 - 291
Copyright
Copyright © Royal Society of Edinburgh 1986

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.)

Article purchase

Temporarily unavailable

References

1Bass, H.. Algebraic K-theory (New York: Benjamin, 1968).Google Scholar
2Cohn, P. M.. On the structure of the GL2 of a ring. Publ. Math. I.H.E.S. 30 (1966), 365–413.CrossRefGoogle Scholar
3Gupta, S. K. and Murthy, M. P.. Susli's work on linear groups over polynomial ringsand Serre problem. ISI Lecture Notes 8 (1980).Google Scholar
4Krusemeyer, M.. Generators for SK1 of plane affine curves. Comm. Algebra 12 (1984), 51–63.CrossRefGoogle Scholar
5Suslin, A. A.. On the structure of the special linear group over polynomial rings. Math. USSR-Izv. 11 (1977), 221–238.CrossRefGoogle Scholar
6Vaserstein, L. N.. On the stabilization of the general linear group over a ring. Math. USSR-Sb. 8 (1969), 383–400.Google Scholar