Theorems · Theorem · commutative algebra

Module.Flat.eqLocus_lTensor_eq

∀ {R : Type u_1} (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (M : Type u_3)
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M] {N : Type u_4}
  {P : Type u_5} [inst_7 : AddCommGroup N] [inst_8 : AddCommGroup P] [inst_9 : Module R N] [inst_10 : Module R P]
  (f g : N →ₗ[R] P) [Module.Flat R M],
  ((TensorProduct.AlgebraTensorModule.lTensor S M) f).eqLocus ((TensorProduct.AlgebraTensorModule.lTensor S M) g) =
    ((TensorProduct.AlgebraTensorModule.lTensor S M) (f.eqLocus g).subtype).range

Defined in

Mathlib.RingTheory.Flat.Equalizer

Cited by

0 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraAddCommGroupModuleModuleIsScalarTowerAddCommGroupAddCommGroupModuleModuleModule.Flat