Theorems · Definition · commutative algebra
Ideal.cotangentToQuotientSquare
{R : Type u} → [inst : CommRing R] → (I : Ideal R) → I.Cotangent →ₗ[R] R ⧸ I ^ 2The inclusion map I ⧸ I ^ 2 to R ⧸ I ^ 2.
- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 88 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.subtypeproof · cited by 480
- Ideal.Cotangentstatement · cited by 68
- Submodule.mapQproof · cited by 28
Cited by8
Results whose statement or proof uses this declaration.
- Ideal.cotangentEquivIdealproof · cited by 3
- Ideal.cotangentToQuotientSquare_injectivestatement and proof · cited by 2
- Ideal.toCotangent_to_quotient_squarestatement · cited by 2
- Ideal.to_quotient_square_comp_toCotangentstatement · cited by 1
- Ideal.tensorCotangentHom_injective_of_flatproof · cited by 0
- Ideal.tensorCotangentHom_surjectiveproof · cited by 0
- Ideal.cotangentEquivIdeal_applystatement · cited by 0
- Ideal.range_cotangentToQuotientSquarestatement and proof · cited by 0