Factorization of Invertible Matrices Over Rings of Stable Rank One

Leonid N. Vaserstein; Ethel Wheland

doi:10.1017/S1446788700029980

Factorization of Invertible Matrices Over Rings of Stable Rank One

Leonid N. Vaserstein
, Ethel Wheland

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	455-460
Number of pages	6
Journal	Journal of the Australian Mathematical Society
Volume	48
Issue number	3
DOIs	https://doi.org/10.1017/S1446788700029980
State	Published - Jun 1990

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Factorization of Invertible Matrices Over Rings of Stable Rank One",

abstract = "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.",

author = "Vaserstein, \{Leonid N.\} and Ethel Wheland",

note = "Funding Information: The research was supported in part by NSF grant DMS 86-20428. {\textcopyright} 1990 Australian Mathematical Society 0263-6115/90 \$A2.00 + 0.00",

year = "1990",

month = jun,

doi = "10.1017/S1446788700029980",

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AU - Vaserstein, Leonid N.

AU - Wheland, Ethel

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N2 - 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.

AB - 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.

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U2 - 10.1017/S1446788700029980

DO - 10.1017/S1446788700029980

M3 - Article

AN - SCOPUS:84971941362

SN - 1446-7887

VL - 48

SP - 455

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JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 3

ER -

Factorization of Invertible Matrices Over Rings of Stable Rank One

Abstract

All Science Journal Classification (ASJC) codes

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