Up to this point you probalby have studied groups, sets with a single binary operation satisfying certain axioms. Now we will turn our interest to the more familiar case of sets with two binary operations, what we will call addition and multiplication.
The most natural algebraic structures to study is the integers with the operations of addition and multiplication. These operations are related to one another by the distributive property. If we consider a set with two such related binary operations satisfying certain axioms, we have an algebraic structure called a ring. In a ring we add and multiply elements such as real numbers, complex numbers, matrices, and functions.
