APPROXIMATELY ARTINIAN(NOETHERIAN)C*-ALGEBRAS  

作　　者：Mohammad ROUZBEHANI Massoud AMINI Mohammad B.ASADI 

机构地区：[1]School of Mathematics,Statistics and Computer Science,College of Science,University of Tehran,Tehran,Iran [2]Department of Mathematics,Faculty of Mathematical Sciences,Tarbiat Modares University,Tehran 14115-134,Iran [3]School of Mathematics,Institute for Research in Fundamental Sciences(IPM),Tehran 19395-5746,Iran

出　　处：《Acta Mathematica Scientia》2024年第6期2485-2497,共13页数学物理学报（B辑英文版）

基　　金：supported by grants from INSF(98029498,99013953);partly supported by a grant from IPM(96430215)。

摘　　要：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 O_(∞)-absorption theorem,and implies that a weakly purely infinite C^(*)-algebra is Noetherian iff every its ideal has a full projection.

关 键 词：C^(*)-algebra graph C^(*)-algebra ARTINIAN NOETHERIAN inductive limit (weakly)purely infinite ideal property 

分 类 号：O15[理学—数学]