Theorems · Theorem · commutative algebra
Ideal.toCotangent_eq_zero
∀ {R : Type u} [inst : CommRing R] (I : Ideal R) (x : ↥I), I.toCotangent x = 0 ↔ ↑x ∈ I ^ 2- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 3 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.
Cites8
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
- Idealstatement and proof · cited by 4,748
- Ideal.Cotangentstatement · cited by 68
- Ideal.toCotangentstatement · cited by 45
- Ideal.mem_toCotangent_kerproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.cotangent_subsingleton_iffproof · cited by 3
- Ideal.Cotangent.smul_eq_zero_of_memproof · cited by 2
- Ideal.cotangentToQuotientSquare_injectiveproof · cited by 2