Theorems · Theorem · commutative algebra

Algebra.Generators.ker_comp_eq_sup

∀ {R : Type u} {S : Type v} {ι : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  {ι' : Type u_3} {T : Type u_7} [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T]
  [inst_6 : IsScalarTower R S T] (Q : Algebra.Generators S T ι') (P : Algebra.Generators R S ι),
  (Q.comp P).ker = Ideal.map (Q.toComp P).toAlgHom P.ker ⊔ Ideal.comap (Q.ofComp P).toAlgHom Q.ker

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

1 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower