The general linear group of polynomial rings over regular rings.

Ton Vorst

doi:10.1080/00927878108822596

The general linear group of polynomial rings over regular rings.

Ton Vorst^*

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

In this note we shall prove for two types of regular rings A that every element of GL_r(A[X₁, …, X_n]) is a product of an element of E_r(A[X₁, …, X_n])(the group of elementary matrices) and an element of GL_r(A), for r ≥ 3 and n arbitrary. This is a kind of GL_r-analogue of results of Lindel and Mohan-Kumar and is an extension of a result of Suslin.

Original language	English
Pages (from-to)	499-509
Number of pages	11
Journal	Communications in Algebra
Volume	9
Issue number	5
DOIs	https://doi.org/10.1080/00927878108822596
Publication status	Published - 1 Jan 1981
Externally published	Yes

Access to Document

10.1080/00927878108822596

Persistent URL (handle)

Persistent link

Cite this

@article{5884a768d36d451089ce92f0d779da28,

title = "The general linear group of polynomial rings over regular rings.",

abstract = "In this note we shall prove for two types of regular rings A that every element of GLr(A[X1, …, Xn]) is a product of an element of Er(A[X1, …, Xn])(the group of elementary matrices) and an element of GLr(A), for r ≥ 3 and n arbitrary. This is a kind of GLr-analogue of results of Lindel and Mohan-Kumar and is an extension of a result of Suslin.",

author = "Ton Vorst",

year = "1981",

month = jan,

day = "1",

doi = "10.1080/00927878108822596",

language = "English",

volume = "9",

pages = "499--509",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

TY - JOUR

T1 - The general linear group of polynomial rings over regular rings.

AU - Vorst, Ton

PY - 1981/1/1

Y1 - 1981/1/1

N2 - In this note we shall prove for two types of regular rings A that every element of GLr(A[X1, …, Xn]) is a product of an element of Er(A[X1, …, Xn])(the group of elementary matrices) and an element of GLr(A), for r ≥ 3 and n arbitrary. This is a kind of GLr-analogue of results of Lindel and Mohan-Kumar and is an extension of a result of Suslin.

AB - In this note we shall prove for two types of regular rings A that every element of GLr(A[X1, …, Xn]) is a product of an element of Er(A[X1, …, Xn])(the group of elementary matrices) and an element of GLr(A), for r ≥ 3 and n arbitrary. This is a kind of GLr-analogue of results of Lindel and Mohan-Kumar and is an extension of a result of Suslin.

UR - https://www.scopus.com/pages/publications/0442309149

UR - https://www.scopus.com/pages/publications/0442309149#tab=citedBy

U2 - 10.1080/00927878108822596

DO - 10.1080/00927878108822596

M3 - Article

AN - SCOPUS:0442309149

SN - 0092-7872

VL - 9

SP - 499

EP - 509

JO - Communications in Algebra

JF - Communications in Algebra

IS - 5

ER -

The general linear group of polynomial rings over regular rings.

Abstract

Access to Document

Persistent URL (handle)

Other files and links

Fingerprint

Cite this