Abstract
Given a unital ring R and a two-sided ideal I of R, we consider the question of determining when a unit of R/I can be lifted to a unit of R. For the wide class of separative exchange ideals I, we show that the only obstruction to lifting invertibles relies on a K-theoretic condition on I. This allows to extend previously known index theories to this context. Using this we can draw consequences for von Neumann regular rings and C*-algebras with real rank zero.
| Original language | English |
|---|---|
| Pages (from-to) | 51-62 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 522 |
| Publication status | Published - 1 Dec 2000 |