On the action of the elementary group on the unimodular rows

Abed Abedelfatah

doi:10.1016/j.jalgebra.2012.05.026

On the action of the elementary group on the unimodular rows

Abed Abedelfatah

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

1 Scopus citations

Abstract

We prove that for any commutative ring R of Krull dimension zero, n≥3 and A=R[X ₁ ^±1,. .,X _k ^±1,X _k+1,. .,X _m], the group E _n(A) acts transitively on Um _n(A). In particular, we obtain that every stably free module over A is free, i.e., A is Hermite ring.

Original language	English
Pages (from-to)	300-304
Number of pages	5
Journal	Journal of Algebra
Volume	368
DOIs	https://doi.org/10.1016/j.jalgebra.2012.05.026
State	Published - 15 Oct 2012
Externally published	Yes

Keywords

Hermite rings
Laurent polynomial rings
Stably free modules
Unimodular rows

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2012.05.026

Cite this

@article{84d761e5e72147bd9ec189e5b0333358,

title = "On the action of the elementary group on the unimodular rows",

abstract = "We prove that for any commutative ring R of Krull dimension zero, n≥3 and A=R[X 1 ±1,. .,X k ±1,X k+1,. .,X m], the group E n(A) acts transitively on Um n(A). In particular, we obtain that every stably free module over A is free, i.e., A is Hermite ring.",

keywords = "Hermite rings, Laurent polynomial rings, Stably free modules, Unimodular rows",

author = "Abed Abedelfatah",

year = "2012",

month = oct,

day = "15",

doi = "10.1016/j.jalgebra.2012.05.026",

language = "English",

volume = "368",

pages = "300--304",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - On the action of the elementary group on the unimodular rows

AU - Abedelfatah, Abed

PY - 2012/10/15

Y1 - 2012/10/15

N2 - We prove that for any commutative ring R of Krull dimension zero, n≥3 and A=R[X 1 ±1,. .,X k ±1,X k+1,. .,X m], the group E n(A) acts transitively on Um n(A). In particular, we obtain that every stably free module over A is free, i.e., A is Hermite ring.

AB - We prove that for any commutative ring R of Krull dimension zero, n≥3 and A=R[X 1 ±1,. .,X k ±1,X k+1,. .,X m], the group E n(A) acts transitively on Um n(A). In particular, we obtain that every stably free module over A is free, i.e., A is Hermite ring.

KW - Hermite rings

KW - Laurent polynomial rings

KW - Stably free modules

KW - Unimodular rows

UR - https://www.scopus.com/pages/publications/84864055589

U2 - 10.1016/j.jalgebra.2012.05.026

DO - 10.1016/j.jalgebra.2012.05.026

M3 - Article

AN - SCOPUS:84864055589

SN - 0021-8693

VL - 368

SP - 300

EP - 304

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On the action of the elementary group on the unimodular rows

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this