Generalized Commutator Formulas

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-p...

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Bibliographic Details
Published in:Communications in algebra Vol. 39; no. 4; pp. 1441 - 1454
Main Authors: Hazrat, R., Zhang, Z.
Format: Journal Article
Language:English
Published: Taylor & Francis Group 21.03.2011
Subjects:
Algebra
Commutators
Congruence subgroups
Elementary subgroup
General linear group
Localization and patching
Normal structure
Sandwich classification theorems
ISSN:0092-7872, 1532-4125
Online Access:Get full text
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Summary: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 which is a generalization of the standard commutator formular. This answers a problem posed by Stepanov and Vavilov.
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ISSN:0092-7872
1532-4125
DOI:10.1080/00927871003738964