Theorems · Theorem · commutative algebra
Ideal.toCotangent_to_quotient_square
∀ {R : Type u} [inst : CommRing R] (I : Ideal R) (x : ↥I),
I.cotangentToQuotientSquare (I.toCotangent x) = (Submodule.mkQ (I ^ 2)) ↑x- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.mkQstatement · cited by 232
- Ideal.Cotangentstatement · cited by 68
- Ideal.toCotangentstatement · cited by 45
- Ideal.cotangentToQuotientSquarestatement · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.cotangentToQuotientSquare_injectiveproof · cited by 2
- Ideal.tensorCotangentHom_injective_of_flatproof · cited by 0