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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Vydáno v:Communications in algebra Ročník 39; číslo 4; s. 1441 - 1454
Hlavní autoři: Hazrat, R., Zhang, Z.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis Group 21.03.2011
Témata:
Algebra
Commutators
Congruence subgroups
Elementary subgroup
General linear group
Localization and patching
Normal structure
Sandwich classification theorems
ISSN:0092-7872, 1532-4125
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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 which is a generalization of the standard commutator formular. This answers a problem posed by Stepanov and Vavilov.
AbstractList {/ampp/image?path=/713597239/935085670/lagb_a_474418_o_um0001.gif} which is a generalization of the standard commutator formular. This answers a problem posed by Stepanov and Vavilov.
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.
Author Hazrat, R.
Zhang, Z.
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  email: zuhong@gmail.com
  organization: Department of Mathematics , Beijing Institute of Technology
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10.1007/BF02684689
10.1007/978-3-662-13152-7
10.1515/crll.1981.322.118
10.1017/S0305004100073436
10.1017/is008008012jkt087
10.1007/BF01389750
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Snippet 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...
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SubjectTerms Algebra
Commutators
Congruence subgroups
Elementary subgroup
General linear group
Localization and patching
Normal structure
Sandwich classification theorems
Title Generalized Commutator Formulas
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