Definition:Subdomain

Definition
Let $\left({R, +, \circ}\right)$ be an algebraic structure with two operations.

A subdomain of $\left({R, +, \circ}\right)$ is a subset $S$ of $R$ such that $\left({S, +_S, \circ_S}\right)$ is an integral domain.

Also known as
Some sources prefer to call this an integral subdomain for clarity of exposition. adopts this convention as appropriate.

Also see

 * Subdomain Test