CHAIN CONDITIONS FOR C＊-ALGEBRAS COMING FROM HILBERT C＊-MODULES  

作　　者：Mahmood POURGHOLAMHOSSEIN Mohammad ROUZBEHANI Massoud AMINI 

机构地区：[1]Department of Mathematics, Faculty of Sciences, University of Qom, Qom, Iran [2]Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran

出　　处：《Acta Mathematica Scientia》2018年第4期1163-1173,共11页数学物理学报（B辑英文版）

摘　　要：In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.

关 键 词：Hilbert C＊-module Noetherian and Artinian C＊-algebras purely infinite C＊-algebras Morita equivalence 

分 类 号：O177.5[理学—数学] O153.3[理学—基础数学]