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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory