Algebraic extension

Definition
Let $$R \le S$$ be commutative unital rings. We say that $$S$$ is an algebraic extension of $$R$$ if for any $$a \in S$$, there exists a polynomial $$p(x) \in R[x]$$ such that $$p(a) = 0$$.

The term algebraic extension is typically used for an algebraic extension of integral domains, or an algebraic field extension

Stronger properties

 * Integral extension
 * Separable algebraic extension
 * Normal algebraic extension