Definition:Subdomain

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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. $\mathsf{Pr} \infty \mathsf{fWiki}$ adopts this convention as appropriate.


Also see


Notes

Some sources insist that $R$ must be a ring for $S$ to be definable as a subdomain, but this limitation can be too restricting.


Sources