# Domain

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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.