On subgroups of GL2 over Banach algebras and von Neumann regular rings which are normalized by elementary matrices

Pere Menal; Leonid N. Vaserstein

doi:10.1016/0021-8693(91)90193-C

On subgroups of GL₂ over Banach algebras and von Neumann regular rings which are normalized by elementary matrices

Pere Menal
, Leonid N. Vaserstein

Mathematics

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

1 Scopus citations

Abstract

Let A be an associative ring with 1 and let E₂A be the group generated by all elementary 2 by 2 matrices over A. In this paper we describe all normal subgroups of E₂A for all von Neumann regular rings A, as well as for a wide class of rings A containing all Banach algebras. For Banach algebras A, the answer involves "quasi-ideals" of A, which replace ideals of A in the similar results for GL_nA, n ≥ 3, obtained previously by the second author.

Original language	English (US)
Pages (from-to)	99-120
Number of pages	22
Journal	Journal of Algebra
Volume	138
Issue number	1
DOIs	https://doi.org/10.1016/0021-8693(91)90193-C
State	Published - Apr 1 1991

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/0021-8693(91)90193-C

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abstract = "Let A be an associative ring with 1 and let E2A be the group generated by all elementary 2 by 2 matrices over A. In this paper we describe all normal subgroups of E2A for all von Neumann regular rings A, as well as for a wide class of rings A containing all Banach algebras. For Banach algebras A, the answer involves {"}quasi-ideals{"} of A, which replace ideals of A in the similar results for GLnA, n ≥ 3, obtained previously by the second author.",

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AU - Vaserstein, Leonid N.

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N2 - Let A be an associative ring with 1 and let E2A be the group generated by all elementary 2 by 2 matrices over A. In this paper we describe all normal subgroups of E2A for all von Neumann regular rings A, as well as for a wide class of rings A containing all Banach algebras. For Banach algebras A, the answer involves "quasi-ideals" of A, which replace ideals of A in the similar results for GLnA, n ≥ 3, obtained previously by the second author.

AB - Let A be an associative ring with 1 and let E2A be the group generated by all elementary 2 by 2 matrices over A. In this paper we describe all normal subgroups of E2A for all von Neumann regular rings A, as well as for a wide class of rings A containing all Banach algebras. For Banach algebras A, the answer involves "quasi-ideals" of A, which replace ideals of A in the similar results for GLnA, n ≥ 3, obtained previously by the second author.

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On subgroups of GL₂ over Banach algebras and von Neumann regular rings which are normalized by elementary matrices

Abstract

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