Primitivity and Simplicity in Nearrings

Abstract

The concept of minimal ideals and minimal left ideals plays a dominant role in ring and nearring theory To study deeper results on this concept demands some powerful tools Therefore the idea of the radical in ring and nearring theory is essential In ring theory one of the importance of the Jacobson radical J(R) lies in the fact that every nil left ideal and every nil right ideal in R is contained in J(R) Nearrings is a generalization of rings which arise naturally from mappings on groups Since every ring is a nearring the true statements in nearrings are useful in ring theory In this article the radicals for nearrings and their good properties will be discussed Moreover some results in noncommutative ring theory will be proved in this article

Date of Award	2020
Original language	English
Supervisor	Wen-Fong Ke (Supervisor)