1999/06/26 by Francesc Perera, Perera, Francesc
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.math/9906181
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.