Theorems · Theorem · commutative algebra
Ideal.cotangentToQuotientSquare_injective
∀ {R : Type u} [inst : CommRing R] (I : Ideal R), Function.Injective ⇑I.cotangentToQuotientSquare- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Cotangentstatement and proof · cited by 68
- injective_iff_map_eq_zeroproof · cited by 62
- Ideal.toCotangentproof · cited by 45
- Submodule.Quotient.mk_eq_zeroproof · cited by 35
- Ideal.toCotangent_surjectiveproof · cited by 15
- Ideal.cotangentToQuotientSquarestatement and proof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.tensorCotangentHom_injective_of_flatproof · cited by 0
- Ideal.tensorCotangentHom_surjectiveproof · cited by 0