Theorems · Theorem · commutative algebra
Derivation.map_one_eq_zero
∀ {R : Type u_1} {A : Type u_2} {M : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring A]
[inst_2 : AddCommMonoid M] [inst_3 : Algebra R A] [inst_4 : Module A M] [inst_5 : Module R M] (D : Derivation R A M),
D 1 = 0- Defined in
- Mathlib.RingTheory.Derivation.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Derivationstatement and proof · cited by 293
- Derivation.map_one_eq_zero'proof · cited by 1
Cited by17
Results whose statement or proof uses this declaration.
- Derivation.map_algebraMapproof · cited by 12
- Derivation.leibniz_powproof · cited by 10
- Derivation.liftKaehlerDifferential_compproof · cited by 6
- Derivation.restrictScalarsproof · cited by 4
- Derivation.leibniz_of_mul_eq_oneproof · cited by 4
- Algebra.Generators.H1Cotangent.δAux_Xproof · cited by 2
- Differential.logDeriv_oneproof · cited by 2
- Derivation.map_natCastproof · cited by 2
- Differential.mapCoeffs_Xproof · cited by 1
- MvPolynomial.pderiv_inl_universalFactorizationMap_Xproof · cited by 1
- MvPolynomial.pderiv_inr_universalFactorizationMap_Xproof · cited by 1
- Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrixproof · cited by 1