Advanced Algebra

This volume continues the algebra material begun in its companion, Basic Algebra, and is aimed at mathematicians of every kind, from students to working researchers. Its later chapters cover modern algebra, with commutative and noncommutative topics handled side by side. Readers are introduced to associative algebras, homological algebra, algebraic number theory, and algebraic geometry.

The text relies on a large number of worked examples and several hundred exercises. Hints or complete solutions are provided for most of the exercises. Read together, the two books show how algebra connects to the rest of mathematics.