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Paper IPM / M / 16211  


Abstract:  
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 Ïunital 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 Aâ
AâZâ
AâOâ. This is a partial extension of Kirchberg's Oâabsorption theorem and Kirchberg's exact embedding theorem. Finally, we show that each Noetherian AFalgebra has a full finitedimensional C*subalgebra.
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