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Integral extension

Definition

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

Note that any integral extension is algebraic.

Metaproperties

Template:Transitive extension property

Any integral extension of an integral extension is an integral extension.