Theorems · Theorem · commutative algebra

Subalgebra.induction_on_adjoin

∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [IsNoetherian R A]
  (P : Subalgebra R A → Prop),
  P ⊥ → (∀ (S : Subalgebra R A) (x : A), P S → P (Algebra.adjoin R (insert x ↑S))) → ∀ (S : Subalgebra R A), P S

Defined in

Mathlib.RingTheory.Adjoin.FG

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraIsNoetherian