The study of noncommutative rings is a major area in modern algebra. The structure theory of noncommutative rings was originally concerned with three parts: The study of semi-simple rings; the study of radical rings; and the construction of rings with given radical and semi-simple factor rings. Recently, this has extended to many new parts: The zero-divisor theory, containing the study of coefficients of zero-dividing polynomials and the study of annihilators over noncommutative rings, that is related to the Koethe's conjecture; the study of nil rings and Jacobson rings; the study of applying ring-theoretic properties to modules; representation theory; the study of relations between algebraic and concepts of other branches (for example, analytic and topological), etc. Thus, noncommutative rings are ubiquitous in mathematics, and occur in numerous sciences.This volume consists of a collection of original articles refereed by world experts that was presented at the Sixth China-Japan-Korea International Conference on Ring Theory. These articles exhibit new ideas, tools and techniques needed for successful research and investigation in noncommutative ring theory, and show the trend of current research. It is a useful resource book for beginners and advanced experts in ring theory.
An Extension of Rings and Hochschild 2-Cocycles (M Tamer Kosan, Tsiu-Kwen Lee and Yiqiang Zhou); A Short Proof that Continuous Modules are Clean (V P Camillo, D Khurana, T Y Lam and W K Nicholson); Notes on Weakly d-Koszul Modules (Jia-Feng Lu and Xiao-Lan Yu); The Galois Map and Its Induced Maps (George Szeto and Lianyong Xue); A Note on Quasi-Johns Rings (Liang Shen); A New Pseudorandom Number Generator AST (Huiling Song); Von Neumann Regular Rings Satisfying Generalized Almost Comparability (Mamoru Kutami); On Symmetric Biderivations of Semiprime Rings (Asma Ali and Faiza Shujat); When Do the Direct Sums of Modules Inherit Certain Properties? (Gangyong Lee, S Tariq Rizvi and Cosmin Roman); Imprimitive Regular Action in the Ring of Integers Modulo n (Juncheol Han, Yang Lee and Sangwon Park); Notes on Simple-Baer Modules and Rings (Lixin Mao); A Note on Prime Rings with Left Derivations (Nadeem Ur Rehman); On Rings in Which Every Ideal is Prime (Hisaya Tsutsui); Rings over which Polynomial Rings are NI (Juncheol Han, Yang Lee and Sung Pil Yang); On the Faith Conjecture (Kiyoichi Oshiro); Study on the Algebraic Structures in Terms of Geometry and Deformation Theory (Fumiya Suenobu and Fujio Kubo); Structures on S G Near-Rings and -Groups (Yong Uk Cho); Some Commutativity Theorems Concerning Additive Mappings and Derivations on Semiprime Rings (Shakir Ali, Basudeb Dhara and Ajda Fosner).