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Paper   IPM / M / 16211
School of Mathematics
  Title:   On finiteness properties of Noetherian (Artinian) C*-algebras
  Author(s):  Massoud Amini (Joint with M. Pourgholamhossein and M. Rouzbehani)
  Status:   Published
  Journal: Linear Multilinear Algebra
  Year:  2020
  Pages:   DOI: 10.1080/03081087.2020.1733458
  Supported by:  IPM
In this article, we present a trichotomy (a division into three classes) on Noetherian and Artinian C*-algebras and obtain some structural results about Noetherian (and/or Artinian) C*-algebras. We show that every Noetherian, purely infinite and σ-unital C*-algebra A is generated as a C*-ideal by a single projection. We show that if A is a purely infinite, nuclear, separable, Noetherian and Artinian C*-algebra, then A≅A⊗Z≅A⊗O∞. This is a partial extension of Kirchberg's O∞-absorption theorem and Kirchberg's exact embedding theorem. Finally, we show that each Noetherian AF-algebra has a full finite-dimensional C*-subalgebra.

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