Mathlib Map

Theorems · Theorem · commutative algebra

IsIntegral.pow_iff

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {x : A} {n : ℕ},
  0 < n → (IsIntegral R (x ^ n) ↔ IsIntegral R x)
Defined in
Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic
Cited by
1 results in Mathlib
Foundations
Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.zariskisMainProperty_iff' · cited by 4Algebra.zariskisMainPrope…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIsIntegral · cited by 427IsIntegralIsIntegral.pow · cited by 12IsIntegral.powIsIntegral.of_pow · cited by 4IsIntegral.of_powIsIntegral.pow_iffCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.