Lifting units modulo exchange ideals and C*-algebras with real rank zero

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28 Citations (Scopus)

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 languageEnglish
Pages (from-to)51-62
JournalJournal fur die Reine und Angewandte Mathematik
Volume522
Publication statusPublished - 1 Dec 2000

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