J Austral Math Soc Ser A 46 pp122--131, 1989.

Length Theorems for the General Linear Group of a Module Over a Local Ring

Erich W. Ellers and Huberta Lausch

Abstract

Let R be a not necessarily commutative local ring, M a free R-module, and p Î GL(M) such that B(p) = im(p- 1) is a subspace of M. Then p = s₁···s_tr where s_i are simple mappings of given types, r is a simple mapping, B(s_i) and B(r) are subspaces, and t £ dim B(p).

1980 AMS Subject Classification (1985 Revision): primary 15A23; secondary 20H15 <\P>

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Authors

Erich W. Ellers

Department of Mathematics, University of Toronto, Toronto, Ontario.

Huberta Lausch

Mathematisches Institut, Universität Würzburg, Am Hubland, D-8700 Würzburg, West Germany.