On The Deformation Of The Polynomial Ring Of Bare And Pp Of The Study

This paper consists of four chapters. The aim of this paper is to study Bare and PP rings ect. of polynomial rings and deformated polynomial rings(Ore extensions, skew power series, generalized power series ect.).In the first chapter, we introduce some concepts, the background of this issue and some results known to all. Then we tell readers what we will do in this paper.In the second chapter, we will study PP and PS rings of Ore extensions. The main work is to generalize one of the results of Chan[12].In the third chapter, we study the annihilator ideals of power series and Ore extensions on noncommutative rings and generalize [13,proposition 3.1]. Then we get Therom 3.1, 3.2, 3.3, 3.4. At the end of this chapter we study the relation of iterated skew polynomial rings and quantum group and got Corollary 3.8, 3.9.In the end, we study Bare and PP rings of generalized power series on commutative and noncommutative rings. Meanwhile, we generalize [26,Th2.3] to noncommutative rings and obtain our Th4.5.