Editing Algebraic integer (section)

===Integral closure===
Every root of a monic polynomial whose coefficients are algebraic integers is itself an algebraic integer. In other words, the algebraic integers form a ring that is [[integrally closed domain|integrally closed]] in any of its extensions.

Again, the proof is analogous to [[Algebraic_number#Algebraic_closure|the corresponding proof]] for [[algebraic number]]s being [[algebraically closed field|algebraically closed]].