Fields

Algebraic structures in mathematics.

In mathematics, fields are algebraic structures consisting of a set equipped with two operations—addition and multiplication—that satisfy specific properties including commutativity, associativity, distributivity, and the existence of additive and multiplicative identities and inverses.

The term 'field' in mathematics comes from the German word 'Körper', introduced by Ernst Kummer.

In math, a field is like a number system where you can add, subtract, multiply, and divide (except by zero) and the rules still work out nicely.

What is a field? A set with addition, subtraction, multiplication, and division operations that follow specific rules
What are examples of fields? Real numbers and complex numbers are common examples
Why are fields important? They provide a framework for solving equations and performing mathematical operations

algebraic structure

real numbers complex numbers finite fields

mathematics