Examples of Groups and Rings

Abstract

This chapter is a survey of the most prominent examples of groups and rings. Roughly speaking, the first half of the chapter is devoted to commutative structures and the second half to noncommutative structures. A ring is, in particular, an additive group, and its invertible elements form a multiplicative group. Examples of rings and groups will therefore be intertwined. One of the goals of the chapter is to show that groups and rings occur throughout mathematics. Exposure to algebraic ideas is therefore useful for mathematicians working in all areas.