C* 代数理论的关系和radical方法
Relation and radical approach to the theory of C*-algebras
摘要：
在本文中，我们追求三个目标。第一部分是应用Amitsur的关系和根理论研究C* 代数A的闭双边理想格Id_{A}。我们表明，许多新的和许多著名的结果C* 代数自然遵循这种方法。利用“关系根”方法，我们考虑所有C* 代数的类A的各种子类，我们称之为C*-性质，因为它们经常与C* 代数的某些性质相联系.我们考虑由CCR-和GCR-代数、具有连续迹的C* 代数-代数、实秩零、AF、核C* 代数-代数等组成的C*-性质P。我们的第二个目标是确定A中属性之间的层次和相互联系。我们的第三个目的是研究格Id_A中关系根与A上拓扑根之间的联系。
英文摘要：
In this paper we pursue three aims. The first one is to apply Amitsur's relations and radicals theory to the study of the lattices Id_{A} of closed two-sided ideals of C*-algebras A. We show that many new and many well-known results about C*-algebras follow naturally from this approach. To use "relation-radical" approach, we consider various subclasses of the class A of all C*-algebras, which we call C*-properties, as they often linked to some properties of C*-algebras. We consider C*-properties P consisting of CCR- and of GCR-algebras; of C*-algebras with continuous trace; of real rank zero, AF, nuclear C*-algebras, etc. Each P defines reflexive relations in all lattices Id_A. Our second aim is to determine the hierarchy and interconnection between properties in A. Our third aim is to study the link between the radicals of relations in the lattices Id_A and the topological radicals on A.
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