Theorems · Inductive type · commutative algebra

Algebra.SubmersivePresentation.HasCoeffs

{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] →
                Algebra.SubmersivePresentation R S ι σ →
                  (R₀ : Type u_5) →
                    [inst_4 : CommRing R₀] →
                      [inst_5 : Algebra R₀ R] → [inst_6 : Algebra R₀ S] → [IsScalarTower R₀ R S] → Prop

A type class witnessing the fact that R₀ contains enough coefficients to descend P to a submersive presentation.

Defined in

Mathlib.RingTheory.Extension.Presentation.Core

Cited by

11 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

CommRingCommRingAlgebraFiniteCommRingAlgebraAlgebraIsScalarTower