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 $R$ with identity $1\neq 0$ without zero divisors: that is, for every $a,b\in R$, if $ab=0$, then $a=0$ or $b=0$.