Domain

A domain is the set of points where a mathematical function is defined. When the function is a function of a complex variable, a domain is usually an open connected set.

Domains are useful in many fields of mathematics, including the study of analytic and harmonic functions.

In algebra, a domain is a commutative ring <math>R</math> with identity <math>1 \neq 0</math> without zero divisors: that is, for every <math>a, b \in R</math>, if <math>ab = 0</math>, then <math>a = 0</math> or <math>b = 0</math>.