Theorems · Definition · algebraic geometry

Algebra.ZariskisMainProperty

(R : Type u_1) → {S : Type u_2} → [inst : CommRing R] → [inst_1 : CommRing S] → [Algebra R S] → Ideal S → Prop

We say that an R algebra S satisfies the Zariski's main property at a prime p of S if there exists r ∉ p in the integral closure S' of R in S, such that S'[1/r] = S[1/r].

Defined in

Mathlib.RingTheory.ZariskisMainTheorem

Cited by

10 results in Mathlib

Foundations

Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra