Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. The focus is on algebraic number theory and algebraic geometry, and the distinctions and influences of each topic on the other. Material vital to the knowledge of the professional mathematician is presented. Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. Together the two books give the reader a global view of algebra and its role in mathematics as a whole. They are suitable as texts in a two-semester advanced undergraduate or first-year graduate sequence in algebra.

Inhalt

Transition to Modern Number Theory.- Wedderburn-Artin Ring Theory.- Brauer Group.- Homological Algebra.- Three Theorems in Algebraic Number Theory.- Reinterpretation with Adeles and Ideles.- Infinite Field Extensions.- Background for Algebraic Geometry.- The Number Theory of Algebraic Curves.- Methods of Algebraic Geometry.