Commutative Conditions Of Rings With Variable Identical Equation

As an important algebraic subject, rings are the base on Algebraic Geometry and Algebraic Number Theory. Rings are concerned about many other subjects With development of science and technology, theory in rings is increasingly accurate and perfect. reliminary results of rings have been applied in practice. Consequencely, property of rings is needed to investigate. Commutativity is one of important properties in rings. Study of commutativity is beneficial to discussion of other properties on rings. At the same time, commutative rings are studied in Commutative Algebra. Therefore, study of commutativity of rings become more and more important.We get some new results on commutativity of rings by studying the Kothe semi-simple ring, semi-prime ring and arbitrary ring. We get some further conclusions on aspects of paticular rings and gain some new conclusions.It consists of there parts. The main results in this paper are as following:In the first chapter show the background and significance of the theories, the internal and external actuality and describe the main results of this paper. It is ready for the following to drawing several conclusions.In the second chapter, first, I give some conceptions and conclusions which are relative to this paper. Second, I put forward and strictly proved one commutative conditions of arbitrary ring are given by studying the Herstein theorem and get a further conclusion based on it.In the third chapter, I study commutative conditions of rings with variable identical equation. It consists of four conclusions. This is the main part of this paper.In this chapter, first, I talkd about two positive integers m and n, put forward and proved some commutative conditions of semi-prime ring and Kothe semi-simple ring. Second, I extended two commutative conditions of semi-prime...