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罢颈迟濒别:听On the stable rank of algebras of bounded holomorphic functions.

Abstract: The concept of the stable rank introduced by Bass plays an important role in some stabilization problems of algebraic K-theory analogous to that of dimension in topology. Despite a simple definition, the stable rank is often quite difficult to calculate even for relatively uncomplicated rings. We present examples of algebras for which the stable rank is computed. Next, we consider a similar problem for algebras of bounded holomorphic functions on Riemann surfaces. The central result in this area is a theorem of Treil asserting that the Bass stable rank of the algebra of bounded holomorphic functions on the open unit disk is 1. We discuss some generalizations of Treil's result.

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