We now give an introduction to another type of algebraic structure, called ring. The exposition here will be faster. The emphasis is on the definition of a ring and a field, understanding the few basic examples, and realising that the concepts of a subring, homomorphism and quotient can be defined in a similar way to groups.

We will see a number of examples of rings in the next section. First we are going to list some basic consequences of the axioms. We note that many basic properties involving (such as , and ) follow from the definition of a group and Theorem 2.8.

Edmund F Robertson

11 September 2006