Semistar Operations on Commutative Rings

In this chapter, we develop the theory of semistar operations on commutative rings and apply the theory to study many important classes of integral domains, such as the Dedekind domains, Prufer domains, UFDs, Krull domains, and PVMDs, along with natural generalizations of these classes of domains to rings with zerodivisors. We postpone the use of local methods until Chapter 3. All rings in Chapters 2– 4 are assumed commutative with identity.