Introductory Survey of Multiplicative Ideal Theory
This chapter provides an overview, without proofs, of multiplicative ideal theory. All of the information presented in this chapter is restated and proved in Chapters 2 and 3 in greater generality. The first section is a survey of the theory of integral domains, introducing some of the theory’s most central concepts and results. The reader may at any time wish to consult the various figures and tables at the end of Section 1.1, which summarize the characterizations of and interrelationships among the various classes of integral domains discussed here. The second section provides many examples and counterexamples. The third section provides a brief preview of the generalizations of Sections 1.1 and 1.2 to rings with zerodivisors that are discussed in Chapters 2 and 3.