Theorems · Theorem · commutative algebra

Algebra.Generators.cotangentRestrict_mk

∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {ι : Type w}
  (P : Algebra.Generators R S ι) {σ : Type u_1} {u : σ → ι} (hu : Function.Injective u) (x : ↥P.ker),
  ⇑((P.cotangentRestrict hu) (Algebra.Extension.Cotangent.mk x)) = fun j =>
    (MvPolynomial.aeval P.val) ((MvPolynomial.pderiv (u j)) ↑x)

Defined in: Mathlib.RingTheory.Extension.Cotangent.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra

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DFunLike.coestatement and proof · cited by 62,936
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
LinearMapstatement · cited by 10,215
Finsuppstatement · cited by 5,255
Idealstatement · cited by 4,748
AlgHomstatement · cited by 3,236
one_mulproof · cited by 2,841
MvPolynomialstatement · cited by 2,140
MvPolynomial.aevalstatement and proof · cited by 298
Derivationstatement · cited by 293

Cited by1

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Algebra.PreSubmersivePresentation.isUnit_jacobian_of_cotangentRestrict_bijectiveproof · cited by 1