Uniform Rings And Uniform Modules

Algebraic subject is an important and basic embranchment of mathematics. It goes through great changes in subjects investigated, methods and central problems. Ring theory as an important algebraic subject is the base of Algebraic Geometry and Algebraic Number Theory. Rings are refered in many other fields. With the continuous development of science and technology, ring theory is increasingly accurate and perfect. results of rings have been applied to practice. In addition, defining rings by modules theory makes discussion much easier in studing methods.In this paper, some properties and theories about uniform rings and uniform modules are discussed, and the relations between uniform rings and uniform modules are abtained. At the same time, special radicals determined by uniform rings classes are given in some special conditions.In order to make the relations and differences between modules and rings clearer, the uniform rings and the uniform modules are discussed by contrast, and some same and similar properties are studied.This paper consists of five parts. The main results are summarized as follows:(1) The main contents of this paper, the background and significance are described;(2) The preparing knowledges of uniform rings and uniform modules are introduced. It is ready for proving several conclusions;(3) The properties of uniform rings are discussed from three aspects of the relations between uniform rings and semiprime rings and prime rings, the essential of uniform rings and regularity of uniform rings;(4) The uniform module is discussed simiply, including the relations between uniform modules and semiprime modules and prime modules, the essential and regularity of uniform modules. In addition, the uniform rings are described by module theory; (5) The two conditions which the uniform rings classes are the special classes in are given. At the same time, the special radicals are established by the special classes.