Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifting units modulo exchange ideals and C*-algebras with real rank zero   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.

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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: acc-phys