Idempotent chains and bounded generation of SL2.

We investigate connections between association chains of idempotents and bounded generation of SL 2 by elementary matrices. This enables us to identify many classes of matrix rings that have universal bounds on the length of association chains. In particular, many matrix rings have the property that every regular element is special clean. We also improve the usual criterion for checking perspectivity via association chains. [ABSTRACT FROM AUTHOR]