Analytic Functions with Ring Theory

Abstract

Complex Analysis is a subject which has something important and interesting for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics like pure mathematics and applied mathematics. We know that the Ring theory have nice properties. In this thesis we will discuss some definitions and notations of some elementary terms like integral domain, ideals, and Maximal ideals. This view of complex analysis and Ring theory the thesis submitted by me has named as Entire functions with Ring theory has influenced me to writing and selection of subjects matter. In each chapter all concepts and definitions have been discussed in detail and in lucid manner i.e clear and easy to understand, so that some one should fell no difficulties. Chapter 1 includes only the introduction of this thesis paper that whatever work done by me and also what is the consequence that how the results are modified simply (no new results) Chapter 2 is the basic of Holomorphic function and Meromorphic functions and Entire function and some definitions are given. By using the definitions of these we will also discussed about Univalent functions and the area theorem and its consequence. Chapter 3 contains the basic idea of preparation for the ideal theory in the rings of Analytic functions and also ideal structure of the rings of Analytic functions. In this chapter we use the concept of divisibility of an integral domain and the theorem based on homomorphism.