Theorems · Definition · commutative algebra

IsStronglyTranscendental

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

We say that x : S is strongly transcendental over R if forall u : S and all p : R[X], p(x) * u = 0 → p * u = 0. If S is a domain, and R ⊆ S, this is equivalent to the image of x in Frac(S) being transcendental over R. See IsStronglyTranscendental.iff_of_isFractionRing.

Defined in

Mathlib.RingTheory.Algebraic.StronglyTranscendental

Cited by

14 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra