Standard

On the word length of commutators in GLn(R). / Sivatski, A. S.; Stepanov, A. V.

в: K-Theory, Том 17, № 4, 01.01.1999, стр. 295-302.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Sivatski, AS & Stepanov, AV 1999, 'On the word length of commutators in GLn(R)', K-Theory, Том. 17, № 4, стр. 295-302. https://doi.org/10.1023/A:1007730801851

APA

Sivatski, A. S., & Stepanov, A. V. (1999). On the word length of commutators in GLn(R). K-Theory, 17(4), 295-302. https://doi.org/10.1023/A:1007730801851

Vancouver

Sivatski AS, Stepanov AV. On the word length of commutators in GLn(R). K-Theory. 1999 Янв. 1;17(4):295-302. https://doi.org/10.1023/A:1007730801851

Author

Sivatski, A. S. ; Stepanov, A. V. / On the word length of commutators in GLn(R). в: K-Theory. 1999 ; Том 17, № 4. стр. 295-302.

BibTeX

@article{304a82dc8a63455ea85b89fd74edc82b,
title = "On the word length of commutators in GLn(R)",
abstract = "Van der Kallen proved that the elementary group En(C[x]) does not have bounded word length with respect to the set of all elementary transvections. Later, Dennis and Vaserstein showed that the same is true, even with respect to the set of all commutators. The natural question is: Does the set of all commutators in En,(R) have bounded word length with all elementary transvections as generators? The article provides a positive answer over a finite-dimensional commutative ring R.",
keywords = "Dimension of maximal spectrum of a ring, Elementary subgroup, General linear group, Word length",
author = "Sivatski, {A. S.} and Stepanov, {A. V.}",
year = "1999",
month = jan,
day = "1",
doi = "10.1023/A:1007730801851",
language = "English",
volume = "17",
pages = "295--302",
journal = "K-Theory",
issn = "0920-3036",
publisher = "Wolters Kluwer",
number = "4",

}

RIS

TY - JOUR

T1 - On the word length of commutators in GLn(R)

AU - Sivatski, A. S.

AU - Stepanov, A. V.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - Van der Kallen proved that the elementary group En(C[x]) does not have bounded word length with respect to the set of all elementary transvections. Later, Dennis and Vaserstein showed that the same is true, even with respect to the set of all commutators. The natural question is: Does the set of all commutators in En,(R) have bounded word length with all elementary transvections as generators? The article provides a positive answer over a finite-dimensional commutative ring R.

AB - Van der Kallen proved that the elementary group En(C[x]) does not have bounded word length with respect to the set of all elementary transvections. Later, Dennis and Vaserstein showed that the same is true, even with respect to the set of all commutators. The natural question is: Does the set of all commutators in En,(R) have bounded word length with all elementary transvections as generators? The article provides a positive answer over a finite-dimensional commutative ring R.

KW - Dimension of maximal spectrum of a ring

KW - Elementary subgroup

KW - General linear group

KW - Word length

UR - http://www.scopus.com/inward/record.url?scp=0013252019&partnerID=8YFLogxK

U2 - 10.1023/A:1007730801851

DO - 10.1023/A:1007730801851

M3 - Article

AN - SCOPUS:0013252019

VL - 17

SP - 295

EP - 302

JO - K-Theory

JF - K-Theory

SN - 0920-3036

IS - 4

ER -

ID: 49794212