Field

Overview

A field is a set with a two operations defined on them. While fairly technical, it is a generalization of the familiar real and complex numbers.

Axioms

A field is a set {% F %} with two laws of composition, {% + %} (addition) and {% \times %} (multiplication).

1. {% F %} is an abelian group with respect to addition. The identity element is labeled {% 0 %}.
2. Multiplication is commutative: {% a \times b = b \times a %}
3. Distributive law : {% a(b+c) = ab + ac %}