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Krull dimension for C*-algebras

  • Mohammad Rouzbehani ORCID logo EMAIL logo , Massoud Amini ORCID logo and Mohammad B. Asadi
Published/Copyright: July 23, 2022
Forum Mathematicum
From the journal Forum Mathematicum Volume 34 Issue 5

Abstract

In this article, we introduce and study the notion of Krull dimension for C*-algebras. We show that every C*-algebra with Krull dimension contains an essential ideal that is a finite direct sum of critical ideals. We show that a C*-algebra with Krull dimension has finite-dimensional center, and conclude that every graph C*-algebra with Krull dimension has real rank zero, and is đ’Ș ∞ -stable in the purely infinite case. We also study the (weak) ideal property for critical C*-algebras.

Keywords: Krull dimension; ideal property; Noetherian C*-algebra; critical C*-algebra; graph C*-algebra
MSC 2010: 46L05; 46L80

Communicated by Siegfried Echterhoff

Funding source: Iran National Science Foundation

Award Identifier / Grant number: 98029498

Award Identifier / Grant number: 99013953

Funding source: Institute for Research in Fundamental Sciences

Award Identifier / Grant number: 96430215

Funding statement: The first and third authors were supported by grants from INSF (Nos. 98029498, 99013953). The second author was partly supported by a grant from IPM (No. 96430215).

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Received: 2021-11-30
Revised: 2022-05-25
Published Online: 2022-07-23
Published in Print: 2022-09-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Recognizing pro-đ–± closures of regular languages
  3. Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups
  4. Non-perturbative graph languages, halting problem and complexity
  5. Spectral synthesis via moment functions on hypergroups
  6. A function field analogue of the Stark conjecture
  7. Continuity properties and Bargmann mappings of quasi-Banach Orlicz modulation spaces
  8. Krull dimension for C*-algebras
  9. The sharp bound of the third Hankel determinant for starlike functions
  10. The role of gentle algebras in higher homological algebra
  11. Classifying spaces for the family of virtually abelian subgroups of orientable 3-manifold groups
  12. L p boundedness for a maximal singular integral operator
  13. Common reducing subspaces and decompositions of contractions
  14. A restriction estimate on Morrey spaces
  15. On ideals in group algebras: An uncertainty principle and the Schur product
  16. Spectrality of self-similar measures with product-form digits
  17. Borderline Lipschitz regularity for bounded minimizers of functionals with (p,q)-growth
  18. On the L q spectra of in-homogeneous self-similar measures
https://doi.org/10.1515/forum-2021-0304
Keywords for this article
Krull dimension; ideal property; Noetherian C*-algebra; critical C*-algebra; graph C*-algebra

Articles in the same Issue

  1. Frontmatter
  2. Recognizing pro-đ–± closures of regular languages
  3. Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups
  4. Non-perturbative graph languages, halting problem and complexity
  5. Spectral synthesis via moment functions on hypergroups
  6. A function field analogue of the Stark conjecture
  7. Continuity properties and Bargmann mappings of quasi-Banach Orlicz modulation spaces
  8. Krull dimension for C*-algebras
  9. The sharp bound of the third Hankel determinant for starlike functions
  10. The role of gentle algebras in higher homological algebra
  11. Classifying spaces for the family of virtually abelian subgroups of orientable 3-manifold groups
  12. L p boundedness for a maximal singular integral operator
  13. Common reducing subspaces and decompositions of contractions
  14. A restriction estimate on Morrey spaces
  15. On ideals in group algebras: An uncertainty principle and the Schur product
  16. Spectrality of self-similar measures with product-form digits
  17. Borderline Lipschitz regularity for bounded minimizers of functionals with (p,q)-growth
  18. On the L q spectra of in-homogeneous self-similar measures
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