### Abstract

Original language | English |
---|---|

Pages (from-to) | 365-381 |

Number of pages | 17 |

Journal | Journal of the London Mathematical Society |

Volume | 85 |

Issue number | 2 |

Early online date | 26 Jan 2012 |

DOIs | |

Publication status | Published - Apr 2012 |

### Fingerprint

### Cite this

_{o}(X)-algebra.

*Journal of the London Mathematical Society*,

*85*(2), 365-381. https://doi.org/10.1112/jlms/jdr053

**Ideals in the multiplier and corona algebras of a C _{o}(X)-algebra.** / Archbold, R. J.; Somerset, D. W. B.

Research output: Contribution to journal › Article

_{o}(X)-algebra',

*Journal of the London Mathematical Society*, vol. 85, no. 2, pp. 365-381. https://doi.org/10.1112/jlms/jdr053

_{o}(X)-algebra. Journal of the London Mathematical Society. 2012 Apr;85(2):365-381. https://doi.org/10.1112/jlms/jdr053

}

TY - JOUR

T1 - Ideals in the multiplier and corona algebras of a Co(X)-algebra

AU - Archbold, R. J.

AU - Somerset, D. W. B.

PY - 2012/4

Y1 - 2012/4

N2 - Let A be a stable, σ-unital C*-algebra which is a C0(X)-algebra, that is, for which there is a continuous map ϕ from Prim(A), the primitive ideal space of A with the hull-kernel topology, to the locally compact Hausdorff space X. We show that there is an injective map L from the lattice of z-ideals of the ring of continuous functions on the completely regular space Im(ϕ) to the lattice of closed ideals of M(A), the multiplier algebra of A. For any two ideals in the range of L, there is a maximal ideal of M(A) containing one but not the other. If Im(ϕ) is infinite, then the corona algebra M(A)/A has at least 2c maximal ideals.

AB - Let A be a stable, σ-unital C*-algebra which is a C0(X)-algebra, that is, for which there is a continuous map ϕ from Prim(A), the primitive ideal space of A with the hull-kernel topology, to the locally compact Hausdorff space X. We show that there is an injective map L from the lattice of z-ideals of the ring of continuous functions on the completely regular space Im(ϕ) to the lattice of closed ideals of M(A), the multiplier algebra of A. For any two ideals in the range of L, there is a maximal ideal of M(A) containing one but not the other. If Im(ϕ) is infinite, then the corona algebra M(A)/A has at least 2c maximal ideals.

U2 - 10.1112/jlms/jdr053

DO - 10.1112/jlms/jdr053

M3 - Article

VL - 85

SP - 365

EP - 381

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 2

ER -