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 $\text{[math]}$ with identity $\text{[math]}$ without zero divisors: that is, for every $\text{[math]}$ , if $\text{[math]}$ , then $\text{[math]}$ or $\text{[math]}$ .