Theorems · Theorem · commutative algebra
Ideal.mk_mem_cotangentIdeal
∀ {R : Type u} [inst : CommRing R] {I : Ideal R} {x : R}, (Ideal.Quotient.mk (I ^ 2)) x ∈ I.cotangentIdeal ↔ x ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 2 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.
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.Quotient.mkstatement and proof · cited by 610
- two_ne_zeroproof · cited by 251
- sub_sub_cancelproof · cited by 105
- sub_memproof · cited by 40
- RingHom.toSemilinearMapproof · cited by 18
- Ideal.pow_le_selfproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Extension.Cotangent.map_toInfinitesimal_bijectiveproof · cited by 1
- Ideal.comap_cotangentIdealproof · cited by 0