Rings: Basic theory

Abstract

Chapters 2, 3, 4, and 5 compose the part of the book devoted to rings. In Chapter 2 the basic structure of the ring is explored using set theoretic concepts in such a manner that we can stress analogies when developing other algebraic structures. In Chapter 3 we develop the natural number system and the integers, and in Chapter 4 we use the natural number system and the integers in a further study of rings including a development of the rational numbers. Chapter 5 treats the ring of polynomials, some special rings, and factorization, field extensions, and complex numbers.