Theorems · Definition · commutative algebra

Algebra.Generators.cMulXSubOneCotangent

{R : Type u_1} →
  (S : Type u_2) →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          (r : R) → [inst_3 : IsLocalization.Away r S] → (Algebra.Generators.localizationAway S r).toExtension.Cotangent

The image of g * X - 1 in I/I² if I is the kernel of the canonical presentation of the localization of S away from g.

Defined in

Mathlib.RingTheory.Smooth.StandardSmoothCotangent

Cited by

11 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIsLocalization.Away