Abstract
Let A be an associative ring with 1 and let E 2 A be the group generated by all elementary 2 by 2 matrices over A. In this paper we describe all normal subgroups of E 2 A 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 n A, n ⩾ 3, obtained previously by the second author.
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