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 which is a generalization of the standard commutator formular. This answers a problem posed by Stepanov and Vavilov.
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