Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.comp_sec
∀ (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]
[inst_7 : Algebra.FormallyUnramified R S] [inst_8 : Algebra.EssFiniteType R S],
TensorProduct.AlgebraTensorModule.lift (↑R (Algebra.lsmul S S M).toLinearMap.flip).flip ∘ₗ
Algebra.FormallyUnramified.sec R S M =
LinearMap.id- Defined in
- Mathlib.RingTheory.Unramified.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- TensorProductstatement and proof · cited by 2,545
- SMulCommClassproof · cited by 1,927
- LinearMap.compstatement · cited by 1,642
- map_zeroproof · cited by 1,614
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRingproof · cited by 1
- Algebra.FormallyUnramified.flat_of_restrictScalarsproof · cited by 0
- Algebra.FormallyUnramified.projective_of_restrictScalarsproof · cited by 0