Theorems · Theorem · commutative algebra
Ideal.cotangentIdeal_square
∀ {R : Type u} [inst : CommRing R] (I : Ideal R), I.cotangentIdeal ^ 2 = ⊥- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 87 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- sub_zeroproof · cited by 938
- Ideal.Quotient.mkproof · cited by 610
- smul_eq_mulproof · cited by 357
- AddMemClass.add_memproof · cited by 229
- eq_bot_iffproof · cited by 159
- pow_twoproof · cited by 150
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.of_comp_surjectiveproof · cited by 6
- Algebra.FormallyUnramified.iff_comp_injective_of_smallproof · cited by 4
- Algebra.Extension.Cotangent.map_toInfinitesimal_bijectiveproof · cited by 1