Theorems · Definition · commutative algebra

Algebra.SubmersivePresentation.basisCotangent

{R : Type u_1} →
  {S : Type u_2} →
    {ι : Type u_3} →
      {σ : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Algebra R S] →
              [inst_3 : Finite σ] →
                (P : Algebra.SubmersivePresentation R S ι σ) → Module.Basis σ S P.toExtension.Cotangent

The classes of P.relation i form a basis of I ⧸ I ^ 2.

Defined in

Mathlib.RingTheory.Smooth.StandardSmoothCotangent

Cited by

2 results in Mathlib

Foundations

Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFinite