A subring$R$ of a commutative ring$S$ is said to be integrally closed in $S$ if whenever $\theta \in S$ and $\theta$ is integral over $R$ then $\theta \in R$
11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers)
13B22 (Commutative rings and algebras :: Ring extensions and related topics :: Integral closure of rings and ideals ; integrally closed rings, related rings )