Definition (integral element):
Let R {\displaystyle R} be a ring, and let S / R {\displaystyle S/R} be a ring extension. An element s ∈ S {\displaystyle s\in S} is called integral over R {\displaystyle R} if there exist elements a 0 , a 1 , … , a n − 1 ∈ R {\displaystyle a_{0},a_{1},\ldots ,a_{n-1}\in R} such that
