Commutators and companion matrices over rings of stable rank 1

L. N. Vaserstein; E. Wheland

doi:10.1016/0024-3795(90)90270-M

Commutators and companion matrices over rings of stable rank 1

L. N. Vaserstein, E. Wheland

Mathematics

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

38 Scopus citations

Abstract

We consider the group GL_nA of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition. We prove that every matrix is similar to the product of a lower and upper triangular matrix, and that it is also the product of two matrices each similar to a companion matrix. We use this to show that, when n≥3 and A is commutative, every matrix in SL_nA is the product of two commutators.

Original language	English (US)
Pages (from-to)	263-277
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	142
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(90)90270-M
State	Published - Dec 1990

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/0024-3795(90)90270-M

Cite this

@article{3d365c98fe68455faaeac020b460869d,

title = "Commutators and companion matrices over rings of stable rank 1",

abstract = "We consider the group GLnA of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition. We prove that every matrix is similar to the product of a lower and upper triangular matrix, and that it is also the product of two matrices each similar to a companion matrix. We use this to show that, when n≥3 and A is commutative, every matrix in SLnA is the product of two commutators.",

author = "Vaserstein, {L. N.} and E. Wheland",

year = "1990",

month = dec,

doi = "10.1016/0024-3795(90)90270-M",

language = "English (US)",

volume = "142",

pages = "263--277",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "C",

}

TY - JOUR

T1 - Commutators and companion matrices over rings of stable rank 1

AU - Vaserstein, L. N.

AU - Wheland, E.

PY - 1990/12

Y1 - 1990/12

N2 - We consider the group GLnA of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition. We prove that every matrix is similar to the product of a lower and upper triangular matrix, and that it is also the product of two matrices each similar to a companion matrix. We use this to show that, when n≥3 and A is commutative, every matrix in SLnA is the product of two commutators.

AB - We consider the group GLnA of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition. We prove that every matrix is similar to the product of a lower and upper triangular matrix, and that it is also the product of two matrices each similar to a companion matrix. We use this to show that, when n≥3 and A is commutative, every matrix in SLnA is the product of two commutators.

UR - http://www.scopus.com/inward/record.url?scp=0043074489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043074489&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(90)90270-M

DO - 10.1016/0024-3795(90)90270-M

M3 - Article

AN - SCOPUS:0043074489

SN - 0024-3795

VL - 142

SP - 263

EP - 277

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Commutators and companion matrices over rings of stable rank 1

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this