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

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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.

Original languageEnglish (US)
Pages (from-to)99-120
Number of pages22
JournalJournal of Algebra
Volume138
Issue number1
DOIs
StatePublished - Apr 1 1991

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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