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Factorization of invertible matrices over rings of stable rank one

Part of: Other groups of matrices Basic linear algebra

Published online by Cambridge University Press:  09 April 2009

Leonid N. Vaserstein  and
Ethel Wheland
Leonid N. Vaserstein
Affiliation:
The Pennsylvania State UniversityUniversity Park, Pennsylvania 16802, U.S.A.
Ethel Wheland
Affiliation:
The Pennsylvania State UniversityUniversity Park, Pennsylvania 16802, U.S.A.
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Abstract

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Every invertible n-by-n matrix over a ring R satisfying the first Bass stable range condition is the product of n simple automorphisms, and there are invertible matrices which cannot be written as the products of a smaller number of simple automorphisms. This generalizes results of Ellers on division rings and local rings.

Keywords

stable rankmodulessimple matrices.

MSC classification

Secondary: 15A23: Factorization of matrices 20H25: Other matrix groups over rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 3 , June 1990 , pp. 455 - 460
Copyright
Copyright © Australian Mathematical Society 1990

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