Field of fractions

A field of fractions is a mathematical system where you can divide any two elements, except division by zero. It extends a base set called an integral domain—like whole numbers—by including fractions (ratios of elements from that set). For example, starting with integers, the field of fractions is the set of rational numbers. This construction allows solving equations involving division and provides a complete framework for many aspects of algebra, ensuring that every possible division (except by zero) is valid within the system.