Generalized commutator formulas

R. Hazrat; Z. Zhang

doi:10.1080/00927871003738964

Generalized commutator formulas

R. Hazrat
, Z. Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Queen's University Belfast

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

24 Citations (Scopus)

Abstract

Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GL_n(A, I) the principal congruence subgroup of level I in GL_n(A), and E_n(A, I) the relative elementary subgroup of level I. Using Bak's localization-patching method, we prove the commutator formula.

Original language	English
Pages (from-to)	1441-1454
Number of pages	14
Journal	Communications in Algebra
Volume	39
Issue number	4
DOIs	https://doi.org/10.1080/00927871003738964
Publication status	Published - Apr 2011

Keywords

Congruence subgroups
Elementary subgroup
General linear group
Localization and patching
Normal structure
Sandwich classification theorems

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10.1080/00927871003738964

Cite this

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title = "Generalized commutator formulas",

abstract = "Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GLn(A, I) the principal congruence subgroup of level I in GLn(A), and En(A, I) the relative elementary subgroup of level I. Using Bak's localization-patching method, we prove the commutator formula.",

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AU - Hazrat, R.

AU - Zhang, Z.

PY - 2011/4

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N2 - Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GLn(A, I) the principal congruence subgroup of level I in GLn(A), and En(A, I) the relative elementary subgroup of level I. Using Bak's localization-patching method, we prove the commutator formula.

AB - Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GLn(A, I) the principal congruence subgroup of level I in GLn(A), and En(A, I) the relative elementary subgroup of level I. Using Bak's localization-patching method, we prove the commutator formula.

KW - Congruence subgroups

KW - Elementary subgroup

KW - General linear group

KW - Localization and patching

KW - Normal structure

KW - Sandwich classification theorems

UR - https://www.scopus.com/pages/publications/79952948818

U2 - 10.1080/00927871003738964

DO - 10.1080/00927871003738964

M3 - Article

AN - SCOPUS:79952948818

SN - 0092-7872

VL - 39

SP - 1441

EP - 1454

JO - Communications in Algebra

JF - Communications in Algebra

IS - 4

ER -

Generalized commutator formulas

Abstract

Keywords

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