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
ACKNOWLEDGMENTS
The first author acknowledges the support of EPSRC first grant scheme EP/D03695X/1. The second author acknowledges the support of NSFC (Grant 10971011). The authors thank Nikolai Vavilov for suggesting the topic of the article to them.
Notes
Communicated by V. A. Artamonov.