Basic Concept Of Binary Composition (Groups, Rings and Fields) : Chapter 5

These are some special types of mathematical systems. The purpose of these is to help in performing certain mathematical operations on a set. In the first three chapters we studied the algebra of certain binary operations and in the fourth chapter we acquainted ourselves with the real number system. Now we take up some mathematical compositions with certain number systems and the binary operations defined on them. The two together form a mathematical system. Before coming to certain special algebraic structures like groups and fields we shall like to discuss binary compositions.

Structure

• Introduction
• Binary Composition
• Various types of Compositions
• Composition Table
• Group
• An Abelian Group
• Properties of a Group
• Modulo
• Rings
• Fields

Objectives: After studying this chapter you should be able to understand:

• Binary composition, various types of compositions, composition table
• Groups, Rings And Fields