Commutativity Of Rings With Constraints On Varying Polynomial Equality

Algebra as a both basic and important subject of mathematics has changed a lot in studying the object, methods of solving problems and central problems. While as an important subject of mathematics, Ring Theory is the base of Algebraic Number Theorey and Algebraic Geometry. Many other subjects are related to Rings. Andcommutativity is one of the important properties of rings.So the study of commutativity is benefical to the discussion of other properties of rings. Therefore, studying the commutativity of rings is very important.With the familiar knowledge of studying commutativity such as nilpotent and radical combining with density theorem ,zero-divisors, the center and subdirectly irreducible ring and so on, this paper studys the constructure of rings with constraints on varying polynomial equality deeply.This article also studys the commutativity of semiprime rings with constraints on varying polynomial equality. Some wider commutative conditions of associative rings are given. Some new conclusions are obtained.This paper is consisted of three parts. The main results of this paper are as follows: Firstly, the background, the purpose of research and significance, the source of topics, the internal and external actuality and the main results of this paper are described.Secondly, some basic definations and relative lemmas are given. Some commutative conditions of semiprime rings are generalized by studying the problem of commutativity of semiprime rings which satisfy varying polynomial equality.At last, the commutative conditions of semiprime rings which satisfy varying polynomial equality are widen on associative rings and more usual commutatity of rings which satisfy varying polynomial equality are discussed in associative rings.