In this article, we introduce and study the class of approximately Artinian (Noetherian) C*-algebras, called AR-algebras (AN-algebras), which is a simultaneous generalization of Artinian (Noetherian) C*-algebras and AF-algebras. We study properties such as the ideal property and topological dimension zero for them. In particular, we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely infinite. This extends the Kirchberg's $\mathcal{O}_\infty$-absorption theorem, and implies that a weakly purely infinite C*-algebra is Noetherian iff every its ideal has a full projection.
Mohammad ROUZBEHANI
,
Massoud AMINI
,
Mohammad B. ASADI
. APPROXIMATELY ARTINIAN (NOETHERIAN) C*-ALGEBRAS[J]. Acta mathematica scientia, Series B, 2024
, 44(6)
: 2485
-2497
.
DOI: 10.1007/s10473-024-0623-z
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