Characterizations of Some Radical Rings and Gamma Rings

Abstract

The present thesis entitled "Characterizations of Some Radical Rings and Gamma Rings" is the outcome of the research by me under the supervision of Dr. A. C. Paul, Professor, Department of Mathematics, University of Rajshahi. The main emphasis of this thesis is to find radical rings. In introduction, we introduce the concepts of the complete thesis. The thesis is of eight chapters. In the first chapter, we discuss the preliminaries of the complete thesis. This chapter is the basic concept of our work. Here we discuss the definitions and some results of /:rings. We develop some characterizations of p-rings in the second chapter and in the third chapter, we generalize the p-rings. We define p-F-ring and prove the analogous properties of p-rings for p-I'-rings in the fourth chapter and the fifth chapter J-I'-rings are the generalizations of p-F-rings. In the sixth chapter, we define the regular /:rings that are more general than that of S. Kyuno, N. Nobusawa and B. Smith [14] and we also develop sufficient conditions for F-rings to be regular. In the seventh chapter, we define an abelian regular F-rings and prove that an abelian regular I'-ring is equivalent to "strongly regular" F-rings. We also develop some other properties. We define unit-regular F-rings in chapter eight and develop a number of equivalent characterizations and also develop a lattice theoretic characterization.