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Theorems · Theorem · commutative algebra

Algebra.FormallyUnramified.lmul_elem

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  [inst_3 : Algebra.FormallyUnramified R S] [inst_4 : Algebra.EssFiniteType R S],
  (Algebra.TensorProduct.lmul' R) (Algebra.FormallyUnramified.elem R S) = 1
Defined in
Mathlib.RingTheory.Unramified.Finite
Cited by
2 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraAlgebra.FormallyUnramifiedAlgebra.EssFiniteType
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.FormallyUnramified.finite_of_free · cited by 7FormallyUnramified.finite…Algebra.FormallyUnramified.comp_sec · cited by 3FormallyUnramified.comp_s…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraAlgHom · cited by 3236AlgHomTensorProduct · cited by 2545TensorProductAlgebra.FormallyUnramified · cited by 75Algebra.FormallyUnramifiedAlgebra.EssFiniteType · cited by 68Algebra.EssFiniteTypeAlgebra.TensorProduct.lmul' · cited by 28TensorProduct.lmul'Algebra.FormallyUnramified.elem · cited by 6FormallyUnramified.elemAlgebra.FormallyUnramified.iff_exists_tensorProduct · cited by 2FormallyUnramified.iff_ex…FormallyUnramified.lmul_elemCITED BYCITES

Cites10

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Cited by2

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