Integrally closed

In mathematics, more specifically in abstract algebra, the concept of integrally closed has three meanings:


 * A commutative ring $$R$$ contained in a commutative ring $$S$$ is said to be integrally closed in $$S$$ if $$R$$ is equal to the integral closure of $$R$$ in $$S$$.
 * An integral domain $$R$$ is said to be integrally closed if it is equal to its integral closure in its field of fractions.
 * An ordered group G is called integrally closed if for all elements a and b of G, if an ≤ b for all natural numbers n then a ≤ 1.