Theorems · Theorem · commutative algebra

Algebra.IsGeometricallyReduced.of_injective

∀ {k : Type u_1} {A : Type u_2} [inst : Field k] [inst_1 : Ring A] [inst_2 : Algebra k A] {B : Type u_3}
  [inst_3 : Ring B] [inst_4 : Algebra k B] (f : A →ₐ[k] B),
  Function.Injective ⇑f → ∀ [Algebra.IsGeometricallyReduced k B], Algebra.IsGeometricallyReduced k A

Defined in

Mathlib.RingTheory.Nilpotent.GeometricallyReduced

Cited by

0 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldRingAlgebraRingAlgebraAlgebra.IsGeometricallyReduced