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

A commutative ring  contained in a commutative ring  is said to be integrally closed in  if  is equal to the integral closure of  in . An integral domain  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.