integral element

noun1

1. •
   Given a commutative unital ring R with extension ring S (i.e., that is a subring of S), any element s ∈ S that is a root of some monic polynomial with coefficients in R.

   • If 𝔖 is the ring of integral elements in a commutative ring 𝔗 (over a subring R) and if the element t of 𝔗 is integral over 𝔖, then t is also integral over R (that is, contained in 𝔖). — 1970