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Length theorems for the general linear group of a module over a local ring

Part of: Other groups of matrices Basic linear algebra

Published online by Cambridge University Press:  09 April 2009

Erich W. Ellers  and
Huberta Lausch
Erich W. Ellers
Affiliation:
Department of MathematicsUniversity of Toronto Toronto, OntarioCanadaM5S 1A1
Huberta Lausch
Affiliation:
Mathematisches Institut, Universität Würzburg, Am Hubland, D-8700 Würzburg, West Germany
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Abstract

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Let R be a not necessarily commutative local ring, M a free R-module, and π ∈ GL(M) such that B(π) = im(π –1)is a subspace of M. Then π = σ1…σtρ, where σi are simple mappings of given types, ρ is a simple mapping, B(sgr;i) and B(ρ) are subspaces and t ≤ dim B(π).

Keywords

local ringsmodulegeneral linear groupfactorzationsimple mapping.

MSC classification

Secondary: 15A23: Factorization of matrices 20H15: Other geometric groups, including crystallographic groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 122 - 131
Copyright
Copyright © Australian Mathematical Society 1989

References

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