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

Francesc Perera

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

Rings and Algebras 2016-09-07 v2 Operator Algebras

Authors: Francesc Perera

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.

Keywords

commutative ring theory c*-algebras monomial ideals

Cite

@article{arxiv.math/9906181,
  title  = {Lifting units modulo exchange ideals and C*-algebras with real rank zero},
  author = {Francesc Perera},
  journal= {arXiv preprint arXiv:math/9906181},
  year   = {2016}
}

Comments

11 pages; to appear in Journal fur die Reine und Angewandte Mathematik

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

Abstract

Keywords

Cite

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