#ring-theory

16. Associative Rings and Algebras

This volume studies rings and algebras with associative multiplication, without requiring commutativity. It develops structure theory, module theory, and connections to representation theory and geometry. Part I. Basic Ring Theory Chapter 1. Rings and Homomorphisms 1.1 Definitions and examples 1.2 Subrings and ideals 1.3 Ring homomorphisms 1.4 Quotient rings 1.5 Basic constructions Chapter 2. Ideals and Structure 2.1 Left, right, and two-sided ideals 2.2 Prime and maximal ideals 2.3 Jacobson...